With DS I had the same low supply issues I had with DD (who was a sloooow feeder too!) but was onto motilium early which gave me good supply, he was a fast feeder, yet things didn't feel quite right. I asked a midwife while still at hospital to check that he didn't have tongue tie or anything and she said no, but didn't even dig around under his tongue. DD would feed with a shield but they confused DS, both were getting bottle top ups and switching easily from breast to bottle and back.
After 5 weeks I knew things should be better so saw a LC. I'd already self diagnosed posterior TT via Dr. Google and she confirmed it. He could poke his tongue out a little, so I think that's why the MW had dismissed TT, but the LC noted that he could not touch the roof of his mouth with his tongue. This made sense as he never did the hungry 'neh' cry (Dunstan Baby Language) like DD did. I thought he had it because if I put a finger in his mouth for him to suck he would suck ok at first, then his tongue would start to slip back and his lower gum would start to contact my finger with each sucking motion.
Getting it snipped at 5.5 weeks is considered a little 'late' to have it done just in the Drs office (but he was still happy to do it). Mostly because bub is strong and doesn't like to be held down for the procedure. DS cried at being wrapped and having his head held, but not when he snipped. There was some blood in his mouth but I fed him right away and all the blood was gone after.
For us, probably because he was older and his muscles were already used to sucking one way, it wasn't like 'wow, that's perfect now' afterwards. But it did help, my nipples were no longer flat after feeds so started to heal quickly. He's 8 months now and feeds like a pro. He still gets bottles too and happily switches between. If you do want to re-establish breastfeeding, I think you should see the expert and then if you get it done see a LC again for help with latching/holds with an older baby.