Is there any budget, high-CRI, AA headlamp?

Echoing some of the comments about taking people’s requirements to heart instead of telling them their requirements don’t make sense. OP knows what they want, and it may not be the same as you.

There was this thread from Sofirn about headlamp development that might be interesting to you. Maybe someday they’ll make one exactly like you want. You can see a few people asking for what you’re asking for, so you’re definitely not alone.

I have a Zebralight AA headlamp, it was a splurge. I also have the $16 Sofirn HS10, a USB-C headlamp that uses 18350 li-ion batteries. The on-body charging makes it convenient to charge since I always have USB-C charging for my phone anyways. It took away a lot of the battery anxiety. It’s also super light weight and if you combine it with a $8 Skilhunt clamp type headband, it’s the perfect combo. The headband it comes with is just OK.