Kuca's even-term conjecture for modified Ulam sequences with fixed even generator

Let $a,b$ be relatively prime, with $a$ even and $b>2a$ odd. The modified Ulam sequence $\mathcal{V}(a,b)$ has explicitly listed even terms in the cases $a\in\{4,6,8,10,12,14,16\}$. Kuca's even-term conjecture. For each listed value of $a$, the displayed list contains all even terms of $\mathcal{V}(a,b)$: for $a=4$, $4,2b,4b+4,12b-4$; for $a=6$, $6,2b,4b+6$; for $a=8$, $8,2b,4b+8,8b+8,24b-8$; for $a=10$, $10,2b,4b+10,8b+10$; for $a=12$, $12,2b,4b+12,8b+12,12b+12,20b+12,28b-12,38b+48$; for $a=14$, $14,2b,4b+14,8b+14,12b+14,22b+14,30b-14$; and for $a=16$, $16,2b,4b+16,8b+16,12b+16,16b+16,24b+16,32b+16,44b-16,44b+16$. These assertions are based entirely on numerical data, and no proof is supplied.