Your post was awhile ago so slightly late response here. Might have already got answers elsewhere. 
“Breaking in” wouldn’t increase termination voltage. Charger chips have a ± 1-1.5% termination accuracy, they are consistent with their termination voltage tho. Your pics show its a tp4056, ± 1.5% accuracy (4.137-4.263v) listed in its datasheet
Interestingly the ML-102 is suppose to have double tp4057 not a single tp4056. With one tp4056 the 1200mA output FT lists is wrong since the chip only claims 1000mA max and HKJ’s sample did only 850mA.
If you wanted to you could replace your chip with one that gets its termination closer to 4.2v. I don’t know if a lot of people would call it “something simple I can change on the PCB” but you do have a hot air station. :bigsmile: You can get tp4056 chips on ebay. £1 for a tp4056 charger board that you can test before transferring the chip.
Your Sanyo 2600s won’t be unhappy or harmed by 4.14v. You just miss a little bit of capacity. Not much I believe.