I need to find a cc that would allow for a 0% transfer fee and ideally 0% APR for some intro period - any options? I already have the Chase Slate which seems to be one of the top recommendations in this regard.
NFCU Platinum, don't think any other major FI is doing both of those atm
You need to be a military or related to join, correct?
BECU, but if you live outside of WA state, it gets tricky should they decide to do verification.
Takes a while, lots of faxing etc
They will frequently ask for POI in addition to ID verification.
Typically this all happens after you've been approved, so if you are not in a hurry and you can be patient, it's an option.
Is there anything out there with 0 - to - sub-3% transfer fee and a reasonably long 0% intro APR?
A variety of responses have been already provided @msavain. The majority of banks such as Citi, BB&T, Discover, etc, are going to have some sort of BT fee, but no lower than 3% in most cases. Your best bet are CUs, such as those mentioned upthread (if you meet membership eligibility), or you can check out the local ones in your area as an alternative.