Agreed! I think a Ruger or Savage in .243 would be "the ticket" for you, especially with bullet restrictions. There are all copper factory loads for this cartridge
https://www.federalpremium.com/rifle/premium-centerfire-rifle/trophy-copper/11-P243TC1.html
I don't know why some folks hold that the .223 won't take coyotes very well. It may be they need to look at a different loading from a different manufacturer, or if they handload they may want a different bullet. HOWEVER since you re in KALIFOЯИIÁ, the bullet restrictions there may cause that round to under perform.
An "upper" in .243, I believe would require an AR-10 platform so you could not buy an "upper" which drops-in to your AR-15, and such an upgrade would be a rather expensive option, much more expensive than the Ruger or Savage option previously mentioned. 7.62x39mm, which you already own, should also do fine on coyotes.
LD