Verify the hammer pin in in the correct position.... The center of the hammer pin should be .625 inch from the top shelf of the lower.
If it's not, get a new lower.
Find a print online and take caliper to check the dimmensions.
Does the bcg go all the way back and forward when the trigger is fully pressed and the disconnecter is holding the hammer back.
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It's supposed to rub - that's how the hammer is cocked - by the carrier. But it's not supposed to restrict it once it's cocked. Do NOT alter the carrier; it's not the leading edge that's causing any issues. Honestly, I'd swap your drop-in trigger with a USGI/standard one to test out, since you already found out that it's the one causing the issue.
There should be no need to polish the carrier for function. The hammer does ride against the carrier, but it should not be felt much after the initial force to cock the hammer.
Your hammer is not able to move far enough past cocked, and / or the trigger pin holes are off.
My vote is for another out of spec 80% lower. That's just a SWAG. #MARRGA
Not the cheapest when you factor in your time...
There looks to be a lot of metal shavings in your picture. I would fully disassemble the lower and clean it out with acetone or alcohol and then as militarymoron mentioned put in a USGI trigger and see if you still have issues.
The OP has been nothing but courteous in his posts.
As far as 'the cheapest stuff,' I may be mistaken but I always thought KAC components were held in pretty high esteem most places. Likewise, the Rise RA-535 may not be my cup o' tea, but it generally has good reviews and isn't cheap at around 230ish.
Obviously the OP has a reason for building an 80% lower, maybe for the challenge of constructing his own, or maybe to be completely off the books, I don't know, but in a world of readily available stripped lowers priced 150.00 and below, I doubt that 'being cheap' was the priority.
The OP came here asking for ideas/help, not a hard time.