The Singapore lounge is not an arrivals lounge, the only arrivals lounges in oneworld are at HKG, LHR T3 and LHR T5 - all of which have different policies depending on airline flown, class and status.
The OP was trying to access the lounge from 2200-2359.. Then go to transit hotel, then out to checkin for his flight... Now normally (if all the flights are on time) I suspect the lounges effectively close at 2300/2330 (last flight being QF1) and the staff are trying to clean up from 2300 onwards.
Once the OP checks in for his JQ flight (3 hrs before), and comes back airside he will not have access (the lounge will be closed)...
The next onward flight has to implicitly have a same day clause, otherwise say on a QF9-QF9 with 3 days break in SIN, you could claim lounge access on the basis of next onward flight