There usually is not a huge difference in terms of admissions chances from Round 1 and Round 2. Earlier is usually better, all things considered, but Round 2 is fine. It's Round 3 and beyond that you want to avoid.
Different people have different approaches for what schools to put in what round. There is some logic in doing your reach and target schools in R1 and safer schools in R2 because most schools require a deposit before R2 notifications come out. If you applied to safe schools first, you might be in a situation where you plunk down 1500 for your safety only to lose it when you're accepted to your target or reach.
If it's just your recommendations that are holding it up, submit your application before the R1 deadline. If for some reason your recs don't get in in time, there's a chance that the school will still consider you for R1, and even if they don't, the worst that happens is you get bumped to R2 anyway.