I hope this doesn't come across as nosy but I just wanted to make sure you cleared the "thickened forumula" with your doctor. Not something that someone should do on their own. But great news about the weight gain!
LLL might be able to help you determine how much she should be eating in a 24-hour period. It's somewhere around 2-2.5 oz per lb of weight. I'd be aiming for 2.5 oz per lb if she's not gaining quite enough. There is such a thing as a "catch-up" amount (that is even higher than 2.5 oz per lb) if she's wasn't at her birth weight at one week.
How did he act after getting a bit of formula? Maybe you can get a before- and after-feeding weight done by a lactation consultant, just to make sure? I mean, if he's pooping that much, it seems like he'd be getting enough but the before- and after-feeding weight might give you some peace of mind or alert you if there are issues.
I'm sorry that I can't remember the optimal levels for nursing off the top of my head but you may want to insist on getting your thyroid levels checked shortly after birth. Maybe 2 weeks out (or sooner if you seem to be struggling with supply in any way) and then again at maybe 6 weeks or 2 months? Try also to remember to take your thyroid medication daily after the birth. We really struggled postpartum and I forgot a few doses and then when I was going to get my...
I used a nipple shield for about 4 months (we did a before and after weight to make sure ds could transfer milk well) and slowly weaned off of it (similar technique to the pp). I told myself if I had to use it the whole time he was bf'ing, I would, and that sorta took the pressure off, ya know? We weaned off when we were both ready with no problems.
Ditto tanyato 100%. I agree that 4 months is not a good age to try and limit night feedings. Sleep can go through a rough stage at that time even without doing anything. If what you are doing is working well, stick with it!