Before you do anything else finish your disassembly and have someone you TRUST measure everything. I know that can be tough to do, but you will save yourself time and money in the long run.
A mm of movement may or may not be bad, but you have to measure the whole bore to make sure it is round and straight.
If you don't have it out, you can not tell if the crank needs ground or not. Sometimes they can simply be polished and be fine.
Patience is your friend.
