How do I transfer photos off my V10 when it is stuck in the boot loop?

I've been down this path with my LG G4 when I had to choose between the phone or the final photos of the cat I can't replace. The problem is these phones have a serious issue with the motherboard that's reportedly due to the PMIC, but the issue with fixing them is you are gambling on if it will be reliable. Consider this fix a TEMPORARY DATA RECOVERY solution, NOT A REPAIR. The problem with repairing them is LG has been vague about the exact cause, so we don’t have anything to work with at a professional level to help folks like you save it beyond speculation, making our best solution data recovery and a new phone from another manufacturer. This refusal to repair them is further supported by the fact you can get a phone from any other manufacturer without this many unknowns, and who will try and do more then LG.

This isn't the first time LG has had issues but the G4/V10 and a few others were class action bad for once. My first LG was stolen before I had to take a hairdryer to it like my G4. Generally, a hot air reflow station is better then a hairdryer but the hairdryer is going to be more common. You can read my procedure here to reflow it and recover your data: How do I get the phone working for data recovery?

The disassembly of your V10 looks similar to my G4 I used to use, but I'd recommend following the guides for the V10 to avoid missing any steps that are different. The G4 was my 2nd and final LG to this very day, and I now buy my phones outright - I haven’t looked back since because phones are too expensive to ignore the risk of a similar flaw coming back and have stood firm on this since 2017.