PSP 1000 battery replacement?

So, i wanna bring my PSP out of the drawer after many years, but having to keep it plugged to play is quite uncomfortable.
The console is CFW'ed and full of games with hours of gameplay, but i wanna be able to take it outside or play on the bed without cables all around me, like it's intended.

The battery swollen and the plastic cracked, the metallic insides exposed and all. Completely unuseable.
I brought a couple chinese ones but they turned out to be total crap, they turn off suddenly, apparently they give uneven voltage. They don't charge right.. total crap

So, my question is, what's the recommended thing to do? a battery mod using LIPO? perhaps a phone battery? Is there any way to do those without removing the UMD reader? not that i ever use it, but i'd like to keep my PSP as untouched as possible. A non destructive external mod would be preferible over a "remove UMD and cut thru all these parts of plastic to fit a huge LIPO

is there any PSP battery i can buy on amazon or whatever that does work reliably? i doubt any of those could be official sony ones because it's been so long even the unopened ones if there's any are too old now i guess.

Anyways, that's all.

 

I won't try luck with these awful chinese ones unless someone assures me that certain brand is reliable. I could do with 2-3 hours of gameplay per charge. It's mostly to avoid being stuck near the plug all the time, i wouldn't take it with me for trips or whatever, probably.
I've been using it without battery, i know. But it kinda ruins the point of it being portable u know?