i didn't do anything special for umbi cord, and clara was fine. i did quite quickly move into small ittis which sat below her stump anyway as they're such low rise, but that was when she was a week or so old... before that it was soggy muslins that i was rubbish at folding so they often went over the stump.
I think if I was doing it again I think I'd be planning on using terries for the first couple of weeks (both of mine were in sposies just for the very beginning ), and then going into smalls (Little Lambs etc.). I never had to change my LOs more than 6 or 7 times a day so it sounds to me like you have plenty (once you get your bamboo terries )... That said, can you ever have enough fluff? These are very cute: