Limited number of variable occurrences in 1-in-3 SAT Is there a known result on complexity class of 1-in-3-SAT with restricted number of variable occurrences? 

I've come up with the following parsimonious reduction with Peter Nightingale,  but I want to cite something if this is known. 

Here is the trick we came up with. This shows that 1-in-3-SAT limited to 3 occurrences per variable is NP complete and #P complete (since 1-in-3-SAT is), while 3-SAT limited to 3 occurrences is in P 

Let’s say we have more than three occurrences of x.  Say we need 6. Then we will introduce 5 new variables x2 to x6 equivalent to x and two new variables d1 and d2 guaranteed to be false with the following 6 new clauses:

x  -x2 d1
x2 -x3 d1
x3 -x4 d1
x4 -x5 d2
x5 -x6 d2
x6 -x  d2


Obviously we replace each occurrence of x after the first one by xi for some i. That gives three occurrences of each xi and d.

The above sets each di to false and all the xi to the same value. To see this, x has to be true or false. If it's true then the first clause sets x2 true and d1 false, and then this propagates down the clasues. If x is false then the last clause sets x6 false and d2 false and it propagates up the clauses. It's obviously strongly parsimonious so preserves counting.
Up to my knowledge the current "limits" have been settled in:

Stefan Porschen, Tatjana Schmidt, Ewald Speckenmeyer, Andreas Wotzlaw:
XSAT and NAE-SAT of linear CNF classes. Discrete Applied Mathematics 167: 1-14 (2014)

See also Schmidt's Thesis: Computational Complexity of SAT, XSAT and NAE-SAT for linear and mixed Horn CNF formulas

Theorem 29. XSAT remains NP-complete for $k$-$CNF^l_+$ and $k$-$CNF^l$, $k, l \geq 3$.

(XSAT for $3$-$CNF^3$ is exactly 1-in-3-SAT where each variable appears exactly $l=3$ times)

Note that the theorem also proves the NP-completeness of the stronger monotone case ($CNF_+$)