I’d like to do it myself, so I’m just wondering if I can solder the balancing leads together in parallel permanently to get the same effect as that parallel charging lead.
You can solder the balancing leads together in parallel.
Make sure your batteries are at the same charge level before doing so.
Bear in mind that you won’t be balancing individual cells, you’ll be balancing parallel sets of two cells.
Lots of people do this without problems though.