Gin-Rummy with different number of cards
The standard 13 Card Rummy suggests you're OK to look to 13 as the basis of your pattern, yes.

For Gin, I'd say you have it right: hands should be 4 + 3*k cards for some positive integer k. 11 is conceivable, but strikes me as too confining.

When adjusting the hand size, you should also adjust the point limit barrier to knock. Since it's 10 points for a 10-card version, you might consider just keeping it the same as the number of cards.