As an Oregon FFL, we have never had to deal with the hunting license issue.
Yessss the 90 days worth of electric bills, rent receipts etc.
We photo copy the "proof of residency" their green card and their valid Oregon drivers license.
We call the 4473 into the State police (Oregon does not use NICS) and in most cases the sale will be delayed a day or two.
We have one client who is a legal alien and buys many guns, his approvals come through within a few minutes to maybe an hour after calling it in.
Not really an issue, just have to keep the paperwork in order is all.
Snowy