Here are my two mixed aviary layouts
1. cockatiels, budgies, Chinese painted quail, zebra finches and diamond doves - never had a problem
2. red-fronted kakarikis, bourke's, red-rumped, zebra finches, collared doves, golden pheasants - also never had a problem!
I have been housing budgies with cockatiels for as long as I can remember and I've never had a problem. You have more cockatiels than budgies so they are less likely to boss them around. I got my first bird, Paulie, many years ago and he was a lutino cockatiel. I built him an aviary and put a breeding pair of budgies in with him, then I got a female cockatiel for Paulie and they too became a breeding pair, then I added another pair of cockatiels AND another pair of budgies and never ever had a problem! I personally think they would be fine and as you said you aren't planning on breeding so there would be no conflict about that.
What do you feed your cockatiels at the moment? If it's a seed mix with fruit and veggies etc provided too then it will be very similar, cockatiel mix is pretty much budgie mix with some sunflower thrown in. The budgies will eat the same food but they wont eat the sunflowers. Every single one of my budgies goes CRAZY for millet, so crazy they even land on me for it.
Budgies are known for bullying other birds but being as the tiels are a lot larger I've never known a problem. Yes they may bicker. My budgies would come bounding up to my cockatiels and they'd get a telling off from the big cresty ones
I think that budgies would be a nice addition for you AND you would be taking in rehomes, which is VERY nice of you