Hi,
I wouldn't suggest you switch wood shavings for fleece as it will prevent them from burrowing or will cause problems if they chew or ingest it. Also, anything fleece-life my hamsters have promptly ripped to shreds to make bedding from.
You could look at the paper based bedding like care fresh? I've not used this personally but the pieces may be slightly larger and therefore harder to kick out of the cage?
My hamsters like to kick out bedding quite often - I have a dust buster for this very purpose
If it's gets too annoying, you may be better with a tank style cage, therefore they cannot kick anything out.