You could hire another shift of support engineers for those times...
- one shift predominantly in UTC-8 -> US West Coast
- one shift predominantly in UTC+8 ~> Singapore/Australia West Coast
- one shift around UTC+0 -> Europe
For 8h days, it works ok. I think that shorter days could work, if the shifts were split. There are also some offices outside of the 3 major time zones, which also fills in gaps.
Of course, dev availability is not usually 24/7 but there are two layers of support before issues reach dev.
Eventually they realized they could just have people on days in the US and an opposite schedule in India instead of three US shifts. But communication certainly didn't improve.