It's not very hard to do at all, actually. Getting the hammers in place is OK, you just have to make sure, as you pick the assembly up to slide the two plates back together, that the two stay firmly together - usually, you can slide the plates together a little way into the tabs before picking it up to do the final shove (and it is a shove!).
The rubber may or may not be a problem. I haven't had a really bad one, so I don't know quite how bad it gets, or how common that actually is. However, if it is bad, it could be contributing to your problem already!
edit: fohat.digs made a very nice
replacement foam mat for his 122-key.
Just remember when you remove the keys, to leave the spacebar on.