Hi
With respect to the target acceptance I just tried a couple of settings to get rid of the target_accept message.
As I understand from the BetaBinomial alpha and beta must be positive.
Don’t they need to be represented by a distribution that is a least truncated at 0?
I played around with an online simulator:
https://www.randomservices.org/random/apps/SpecialSimulator.html
That sets the range of alpha and beta from 0 to 50.
So I just took that same range.
But I am a bit of a dummy 
Regards Hans