A similar situation for me, with my current plans. I'm thinking of flying:

Day 1
LH LIS-FRA (same-day connection at FRA)
SQ FRA-SIN (arriving 0635)

Day 2
UA SIN-HKG (departing next day at 0640)
OZ HKG-ICN (same-day connection)

Since the UA flight is so early at 0640, I'd like to spend the night in the Transit Hotel, which means I need my UA boarding pass to get back into the secure zone when I come back to Changi at the end of Day 1.

From what I can tell so far, there are a number of possibilities for obtaining my UA boarding pass:

1. SQ check-in at FRA might be able to issue the connecting UA boarding pass
2. UA transfer desk at FRA might be able to issue it
3. UA transfer desk might be still open when I arrive at 0635 (assuming on time)
4. UA has a ticket desk in the check-in area, which presumably also has the capability of printing BPs.

Ideally my SQ flight will arrive within time in order to go to the UA transfer desk at SIN, but given that is not guaranteed, what are my chances of any of the others being successful?