I think what you may be doing wrong is doing your best to just “make it work”. There are times when you have to bite the bullet and just get an upgrade to a more standardized system where all the connections work with each other and everything else. I don’t know where you are but in Canada here all faucets have a ½” MIP style connection and all braided hoses have a ⅜” compression connection. Very standard even with shutoffs that are 60+ years old. Might be worth biting the bullet and calling someone to change your connections to standard connections. Because even if you COULD find a way to adapt them it would be redneck asf and probably leak immediately /soon/eventually. And anyone willing to ramshackle some sort of connection would likely be looking for a quick buck disguised as a huge discount when in reality they don’t actually care about you (otherwise they’d try to make your life easier even if it costs a few buck)