This is old, but it maight give you some ideas.
I have an S4 Plus V2 charger. I think the only 21700 button top USB rechargeable cell that I have (The Cyansky branded BL2150U) fits into it , but just barely. I mean I have to apply some force to get it to seat in there. A quick measure with just a ruler shows about 77.4 +/- 2 mm. (EDIT: Cynasky says 77.3mm. So I was pretty darn close.) Your cell specs say 76.8 mm. So the S4 plus should be able to fit it. It is a decent charger and often recommended around here. There are a couple of lengthy threads about the V2 and new V3 models here if you want to check them out.