Wow - you’re not competitive? Hmmmm - on what earth 
Seems like you are very competitive to me.
So you mention $25K - so that’s the first place to start. You can definitely get there with public schools and the crazy merit they’ll throw at someone like you.
Look at the net price calculators of the privates you mentioned - Harvey Mudd, Cornell, etc. Do they show you at $25,000? If not, then can you afford what they say? If not, they’re likely not worth apps.
For engineering, you likely need to go to a mainstream school but you’d find Christian life there - you may look at WUE schools if you want to go out of state. Or a school like Arizona where you’d get great merit to hopefully get you at about $25K. There are others out of state as well where you can get $20K or less but assuming you want to stay out West (as your list is CA), no need to go there.
You can also look at Christian schools with ABET accredited engineering - but again, you need to run the net price calculators - a Calvin University for example. But again, as a private, you will need to run an NPC.
Good luck.