Itti bittis are a nice compact nappy. You could get a fitted one and just use one of your covers. And a side-snapping nappy we like here is the bubba J pocket - it's fairly inexpensive too from memory... It's also pretty compact. We also like blueberries. Natty has pretty skinny legs though, so not sure if what we like would be what you would like, KWIM? FWIW, I think berry plush are pretty but I don't like the fit of them on my kid either. (I haven't tried cloth on Phoebe yet! I've been way slack.)
The other naps I really like are bubblebubs AIOs.
I think it's probably going to be trial and error though - no one can guess what's going to fit your bub best.