Hey again man,
Don’t beat yourself up in regards to the USB, You have to do it wrong the first time to get it right the next time 
Agree with Insomniac using low melt solder on the through hole portion of the USB, then use a chunky tip and wick out the low melt so the holes are clear (or near clear) , then as Insomniac said hot air on the board directly below the pins, very roughly (depends on your station cal) a temp of 320C and lowest air won’t melt the USB, but it’s directly proportional to air speed, 150C max air will melt them if that makes sense. Then just a case of prepping the pads and going in reverse, it also helps to tin the inner USB pins/pads directly if your finding you can’t get enough solder on the boards pads and doubly ensures a good reflow operation.
You can get metre lengths of low melt solder on eBay for a few quid from UK sellers which is of better quality than the Chinese claimed alloys, it doesn’t typically come flux cored so you have to add quite a bit of flux externally
You can get a big roll of the chipquik 63/37 stuff for about 13 quid (last I checked) on Mouser, can add a few more bits and bobs and get free delivery for orders over 30 i think
Solder suckers wont help you here unfortunately, at least in my experience, decent wick will be a good call, saturate it in flux prior to hitting it with the iron on top.
Avoid using low melt as a substitute for regular leaded solder on the pads and through hole portions when prepping to put the connector back on, low melt doesn’t have the strength or current carying capabilities of standard leaded.
I think a lot of your troubles are related to your soldering iron, I would recommend something like this
https://www.aliexpress.com/item/32820505482.html?spm=a2g0o.productlist.0.0.5779d793eFxjOt&algo_pvid=0963fcbb-47dc-4a17-9a8d-2d4e2fc7f7a6&algo_exp_id=0963fcbb-47dc-4a17-9a8d-2d4e2fc7f7a6-0
though be warned I here they are now coming with a dodgy FW preinstalled, and it seems up in the air which one they ship it with (despite what the listing might say) and it will require some manual work to resolve by flashing a CFW to it, I’d go for the SS or alu handle type version
I use a JL02 type tip (which is one of the T12 finest types) and have no issues prepping the USB pads with just that at 420C so should be a good choice for you 
So the EMMC is the storage for the OS, without it the console won’t boot or fast charge. did you check the LCD connector for bent pins? as if I remember correctly it was 0.4A prior to reassembly in the case?