Is it possible to apply a bounding polygon to a changeset before applying it?

Do not clip the planet after applying diff; clip it while doing so. Most of the time spent doing this is very likely the reading and writing of the data. Your toolchain seems esoteric to me; what people would usually do to solve your problem is (all on one line, written here on multiple lines for clarity)

osmosis
   --read-replication-interval
   --read-pbf mylocalregion.osm.pbf
   --apply-diff
   --bp file=bounds.poly
   --write-pbf mylocalregion-new.osm.pbf

This is extremely unlikely to take six hours even on small hardware! Working with .osm.pbf files (and not with .osm.bz2 files or plain .osm files) is essential here for speed; if your CPU is particularly weak then adding "compress=none" to the write-pbf task could also improve things.

Before you can run Osmosis in the above fashion you will have to initialize the replication loading (--rrii, and modify configuration.txt if you want hourly or daily updates). You can of course download the diffs your way too and then replace the --read-replication-interval with a --read-xml-change myfile.osc.