The latter – when the SNA fails to clear for the highest room type, add room types to your request. The SNA process runs at 2pm hotel time at T-5, T-4, T-3, T-2, and T-1 before arrival so those are your opportunities to modify your request.

For what it's worth, the SNA process will clear you into the highest requested room category that's available. If I were you, I'd just request all room categories you'd be happy to use the SNA on and be done with it. The only way you'd miss out on the highest room category is if it's not available at T-5, your SNA clears to another room type, and then the highest room category becomes available at some point later. It's possible but rather unlikely.