Given your budget, you might look at the WUE. I’m not quite sure of the engineering discipline you’d want - but for mechanical, the following are ABET accredited and some are less difficult admits. That said, engineering has the amongst the highest drop out rate of any major - some studies show over 50% - so your student will need to be really, really strong at math. Given the ADHD, perhaps a smaller school is better. On the flip side, having a school with a lot of majors, just in case also matters.
Here are WUE schools - I removed any that are not ABET accredited - they offer you huge discounts and most are “safe” admits. A few schools (like Oregon State) don’t give to all. Some on the list are small - including the Mining named schools in SD and New Mexco - perhaps that’d be smaller classes?
Alaska: U of Alaska Anchorage, U of Alaska Fairbanks
California: Chico State, Cal State Northridge, UC Merced, Cal Poly Pomona, Cal State Maritime, Cal State Sacramento
Colorado: U of Colorado at Colorado Springs, U of Colorado Denver, Colorado Mesa
Hawaii: U of Hawaii
Idaho: Boise State, U of Idaho, Idaho State
Montana: Montana State and Montana Tech
Nevada: UNLV and Nevada Reno
New Mexico: UNM, NMSU, New Mexico Mining & Tech
N Dakota: NDSU, UND
Oregon: Oregon State, Oregon Tech, Portland State
S Dakota: SD State, SD Mines
Utah: Southern Utah, Utah State, Utah Valley, Utah, Weber State
Wyoming - U of Wyoming
As far as in state goes - E Washington, UW Bothell, WSU, WSU Vancouver, and UW are ABET…as is Seattle U (private but with aid)??
WWU does not offer mechanical engieering so it would not make a wise choice for your son’s interests.
Hopefully that’s some new names to work with - most all will be safeties and all should be in budget.
Best of luck.