Is there any character with radical 月 that has a meaning of 月 (not 肉)? Is there any character with radical 月 that has a meaning of 月 (not 肉)?

What I can find is 期，阴，and 胜，
@OmniBus "those modern fonts are terrible and distinct nothing"—you may despise modern fonts all you like, but when you pick up any calligraphy collection (書法字典) you will find abundant evidence that you'll have to extend your despisal to such names like 王羲之, 歐陽詢, 唐太宗 and so on, as they did not make those distinctions. Also, where the typographic distinction is today made between the different origins of the shape 月, it can be attributed to the influential Kangxi Dictionary of 1716; now, that very dictionary starts with an Imperial Preface which was penned by an eminent member of the Hanlin Academy and, as such, also has 'model character' (Modellcharakter). That writing style is a very orderly Regular script, is full of abbreviated and variant forms, and completely disregards the distinctions between the different origins of 月! This is a fact that most people conveniently gloss over.

I used to think myself that those fonts / writing styles that do distinguish between the different origins of what today is mostly indistinguishable from 月 are more 'correct'; however, i've since changed my mind. 俞佩琳 has argued extensively and convincingly in his 1989 book 《中文字序學》 that efforts to distinguish between the different origins of 月—which goes back to earlier forms of 月 itself and 肉, 舟, and 丹—have been made at several points in Chinese history (most notably the Tang and Qing dynasties), were misguided, and have failed. In modern times, the ROC Ministry of Education tries to promote a 'correct' form of writing along these lines. 

The efforts were and are misguided because modern writing (Kaishu style) is not equal to ancient writing (Seal script and Clerical script); it has evolved and replaces many older forms with simpler equivalents. It is also misguided because the calligraphic means used to make the distinctions—using two horizontal strokes that connect to left and right, or else two short horizontal strokes with gaps on the right, or else two dots, or else a dot and and upward stroke—are not very obviously connected to the outlines of 月, 肉, 舟, and 丹, but arbitrarily chosen expedients. The differences are visually minuscule and hard to remember. In fact, the distinction seems to be objectively difficult; 俞佩琳 adduces many examples that clearly demonstrate that even the editors of the 《五經文字》—the first work that embarked on this particular strain of resurrecting correct forms modeled on Seal script—get it plain wrong in many cases! Clearly, if they can't do it, how could the average writer?

Maybe the reforms could have caught on if the reformers had decided to resurrect 肉, 舟, and 丹 to their full forms in characters like 前, for which we could write ⿱䒑—but then 䒑 is an abbreviation too! In this case, it stands in for 止, so we should really be writing ⿱止. But wait a moment, 刂 is really short for 刀, right, so the 'correct' way to write 前 is, indeed, ! Then again, at least the Small Seal form that is quoted in the Shuowen does not have a 刀; instead, it corresponds to 歬 (be it said that the Small Seal characters as we have them today may not be entirely the original ones, as we do not have an original copy of the work; also, the Shuowen, valuable as it is, contains many known erroneous Seal characters and wrong interpretations of correct forms). It's easy to see where this leads, namely more—many, many more—variant forms. But the pertinent point here is that those who insist on writing 前 with a double-dotted 月 have picked out a pet peeve, a 'perceived historical mistake' that they try to correct, leaving other, equally obvious developments untouched, with no clear reason why (in this case) 舟 should be restored but not 止. If i wanted to describe this with the most flattering terms, i'd call it hyper-correct.

And this is really the problem with trying to revive seal characters in modern writing forms: one may deplore that many useful distinctions in the old characters have been lost in modern script (Wieger's Chinese Characters is almost exclusively dedicated to this cause), but one the other hand, trying to do so would radically change thousands of Chinese characters as we know them today. Just to distinguish 月, 肉, 舟, and 丹 (and a few other components) is a rather arbitrary choice; in fact, many, many distinctions have been lost—or rather, at some point in history that predates the Qin dynasty's unification of the script, purposefully been thrown overboard when the Clerical script was developed. The entire program in the development of Clerical script (and, later, of Regular script) was to simplify Seal characters by simplifying single strokes and writing simpler outlines where possible (about Clerical script antedating Qin Small seal characters there's an interesting video in Chinese; this view is somewhat novel as the relevant bamboo and wood slips were only unearthed during the last century).

This, by the way, is how people came to write 人 as 亻 when occurring on the left hand side; before that was started, there was no such distinction. So when resurrecting old character forms, one should, once more, go all the way and stop distinguishing 人 and 亻! 

It is interesting to see how the afore-mentioned ROC MOE also falls short in its efforts to promulgate a purportedly more 'correct' from of writing, as has been commented on the web:

國字標準字體嚴格區分在小篆中有區別的部件，但有些做法似乎並不一致而令人疑惑。例如「月」字旁與「肉」字旁在楷書中已經合流，都寫做「月」，而國字標準字體則是特別規定代表「肉」字的「月」要將中間兩橫寫成點與挑（見右圖），以示區別（這種做法也有討論空間）。然而，「朝」、「服」等字的「月」字旁其實也不是「月亮」的「月」，而是「舟」字，古代印刷體有將中間兩橫寫為兩點的，以便與「月」保持區別，但是國字標準字體卻完全不區分「舟」字旁與「月」字旁。

What sets apart the MOE 'standard' forms from other sources is the surprising fact that it only distinguishes 肉 and 月, but the 月-like component in 青 is still written with two horizontals; thus, the singular distinction they do make appears ever the more arbitrary, artificial, and hard to justify. Moreover, in both the Regular and Song typefaces, 月 is written with a slanting, not a straight initial stroke where it appears in the bottom part of a character (as in 青, 膏); checking this against classical samples of calligraphy shows this is wrong—月 should appear as ⺝ when in bottom position. Incidentally, ⺝ is also how 月 is written in both the preface and the main part of the Kangxi dictionary! 

As an aside, the Song typeface that is depicted e.g. on http://www.edu.tw/files/site_content/M0001/sungti/as30.htm?open is incredibly ugly and should definitely not be used as an exemplar for what Chinese characters should look like. To be clear: the typeface is proportioned so poorly and its technical defects are so blatantly obvious that any book on the subject of Chinese typefaces, character forms or Chinese fonts should warn against its use.

To this one could add that as for 朋, both chineseetymology and zdic agree that the shape 月 here originated from something different altogether (and it's not 貝, although it still could depict cowrie shells on a string). Writing 朋 with the two-dotted form of 月 makes it look like 朋 was derived from ⿰舟舟, which is patently wrong according to this data. 

What's even worse, when you research character origins, you often get conflicting views. For example, for 胜 the Shuowen says 从肉生聲; another source has 从力朕声 (with 朕 being traced back to ; note that关 is actually ⿱䒑大, from older ⿱火廾), and there is a variant  which the Kangxi Dictionary comments as 古文勝(胜)字, so according to which source you want to trust, you end up with 月 originating in either 肉 or 舟. Likewise, 朝 is variously explained as 从倝舟聲 and as 从日在草中从月. The pretty thought-out device of distinguishing four forms for what had once unambiguously become 月 in the Regular style of China's most renowned calligraphers is at the very least insufficient—many more forms are needed because (1) there are more than four sources for modern 月, and (2) some characters are analyzed differently by different authorities, so we need at least one more form to indicate all cases of doubt.