That sounds like a good idea. I'd get a bamboo Baby Beehinds if I was you, they are more absorbant in my opinion. If they aren't good enough for night you will be able to use it for day sleeps anyway.
Make sure you remember to get some stuffers for the pocket as well. Have you already got boosters/trifolds? The
bamboo fold ups from Baby beehinds would be okay to use as a trifold (since you will be ordering from there anyway

)
Greenkids bamboo inserts are good too especially combined with the microfibre insert not sure of the fit in the MM fleece pockets though maybe you could ask in brand help.
Hope you have some sucess with cloth for nights !