Might not solve the problem, but might help the $$. In our family, everyone (well, almost everyone...some seem to NEVER buy kid-gifts) who is 18+ buys small gifts for everyone under 18. The 18+ people are in an "adult" drawing, but teenagers are allowed to opt into the drawing. THe adult drawing is for a $25-50 gift. The kid-gifts are almost always under $10 each. Often under $5. A book, a small baby toy, a new hat/gloves, a bag with flavored lip glosses, etc.
So for 12-14 kids, one might spend $100-120 TOTAL. And each kid gets SOMETHING to open, going home with a kind of "gift bag" of assorted small items. Makes it fun, but breaks no bank.
To clarify, my aunt/uncle have 2 kids (both young adults now). They don't EACH buy for each kid, they buy as a family. Another family member and her dh have only bought like once EVER ... but everyone still gives little gifts to her son each year.
Then again, though, our family is VERRRRRY loosey goosey about gift-giving. So many have been through severe financial hardship in one year or another that nobody questions, nobody gets offended, and as long as they each end up with a few little trinkets, the kids don't compare gifts with each other and get upset if they "got less." Heck, as a mother, I don't even try to "even up" the gifts among my OWN children. It all comes out in the wash, I'm pretty sure.
Now if yours is a $25-50 per KID gift, it's a totally different thing. Maybe you can just reduce the amount spent per kid gift. Then it's mathematically much less different.
DD12 says last year, she came home from the extended family Christmas gathering with a bag of little things that included Lip Smackers lip glossx2, a white knit hat & gloves set, a paperback book, a new diary, a set of butterfly hair clips, a 500 pc jigsaw puzzle, a set of thin markers and plain paper, and a bottle of bubble bath. NOTHING in there cost $10 but she was happy as a clam.