Agree with getting an oral review, not just tt second opinion. Try to get them to feel the suck on a finger if possible as you did.
Plenty of babies do nurse more at night. I was up every hour or two hours last night form 9pm - 6am with my 5 month old if. But there is a problem there re the weight loss.
I've tried exagg attachment when pain from tt was excruciating and did find it good to ensure he sucked better. YOu basically don't just aim the nipple upwards, you aim it almost backwards into the mouth and flick it in. Then they get a really good wodge of boob and not just nipple.
By the time our tt was seen to I think my son had started to feed badly and I was in pain on one side for months (still am, though less). Time can fix some of these things, if no one else can help you (e,g, no experts nearby). This is why i contacted Jack Newman. So you may decide to persevere with mixed feeding and he may just learn / decide to nurse during the day. 5 months later, my son nurses better but still oddly. I never weighed him though as I got really obsessed with weighing the first one and have been going on how he looks and how others say he looks. Haven't had any weight loss issues though.
I would've thought you'd probably have bad pain from a tt but I don't think you mention it. And if he nurses ok at night, no I wouldn't say it's consistent with tt.
It's pot luck with the helplines - some volunteers are brilliant, some not. You often get different people, so i'd keep trying. Maybe video part of a feed and send it to them - ask them to send it round their volunteers for for advice / feedback. Be sure to mention you've already fed 3 succesfully.
"LC told me on the phone that I didn't have enough milk and to give him formula. My issue was that she never watched me try to feed him or anything before telling me that." Forget and ignore him / her. Totally ludicrous. "YOu don't have enough milk" is defeatist, demeaning, and gives no explanation. Very few women as I understand it just "don't have enough milk". We are biologically designed to be able to feed twins if necessary! Usually it's a question of sth wrong with the suck or the women gives a substitute / puts the baby to the breast infrequently that causes diminishment of supply.
When you've fixed the problem, if you want to decrease formula, increase frequency at the breast and try a Supplementary Nursing Sytem (SNS), e.g. from Medela. I restarted bf my first after 5 weeks totally dry and taught myself to use this and my top tip is breastfeed the baby first THEN use the SNS until they don't want any more formula from it. If he will feed that way if definitely beats syringe feeding - he stimulates the breast, you get to b'f him and he gets forumla from the SNS.