Very small and replaceable battery are two incredibly rare things these days, you almost need to pick one. Same with unlockable loader. Looks like you're dealing with a GSM carrier, so I'll be dealing with US GSM model numbers.
The phones I've been recommending lately "fitting your dimensions" have been the G4 Play (unlocked XT1607) and E4 (unlocked XT1768) as they tick off everything from your list but size. Both will be slightly bigger/around the same size as the Moto G 4G (first or second gen) you're already using, unless you actually meant Moto G4 in which case they will be a bit smaller. Yeah, handset size is getting ridiculous, and it's partly due to antenna band proliferation support, battery life, and a vicious feedback loop between battery life and screen size.
Now, this is an important point. Are you dealing with AT&T or T-Mobile as your primary carrier with your desire to get an LTE handset? If AT&T, you should have the freedom to do what you want and everything should be hunky dory. If T-Mobile and you're needing LTE to get back voice coverage, it's important to know a couple things. 1) Without 700MHz LTE band 12 VoLTE "certified" calling support with T-Mobile, you'll only get voice calling support with any phone on their remaining legacy 2G GSM network in most of the country. 2) Because of point one, they've basically locked out third party ROM support. Flash a third party ROM? Lose VoLTE calling. Just some points of academic curiosity.
As much as I loathe AT&T and won't do business with them directly anymore, they're honestly the least terrible carrier in the nation right now... which is saying something. If you're partly doing this (beyond replacing a fried device) for improved T-Mobile voice calling support, consider porting your number to an AT&T MVNO during your device change if you'd like to keep your handset freedom.
