Hopefully the compressions will help. It sounds like he needs some encouragement to actively suck at the breast for longer periods. Do you have another weight check scheduled? If you go back to the LC, I'd suggest doing a before and after weigh to see how much he's taking. Nipple shields *can* sometimes interfere with transfer of milk, but when used correctly they can also be an effective tool for a baby who can't/won't latch without one. I'd also suggest trying to get in a couple more feeds per day (which it sounds like you may already be doing this since you said you are waking him at night). Then general number of feeds is 8-12 per 24 hours, and with a slow gaining baby its better to aim for the top of that frequency rather than the low end. Personally, I wouldn't start solids that early. If he needs more than he can get from the breast, I'd try to pump and offer EBM as a supplement. BUT, since he is at least *maintaining* weight with BF only, just not gaining, I think its very likely you can get things on track for normal weight gain with a little more work on his BFing (the compressions, more feedings, etc.).
Let us know how its going! Hang in there. You are doing a great job!