If he was raised on rats, understand that mice do smell (& presumably) taste different. That's probably a big part of this- you seem to be switching back & forth?
Also the temperature- so between the different scent & prey that quickly cools to an UN-lifelike temperature, that's likely what is wrong, though your method of prepping & offering f/t sounds okay to me.
An oncoming shed would also be likely to make him hesitant to eat- usually best to wait to feed when you see signs of any snake being in shed.
I can tell you for sure that MANY others have similar feeding issues- BPs aren't the easiest snakes to feed, unfortunately. You just have to keep at it- you've only had him for a month- be patient.