Yes, they can arrive on May 4th. Here is how:
Fly Thai Airways International 990 leaving Auckland on May 3rd at 1:15 pm and arriving in Bangkok at 9:00 pm
Fly Bangkok Airway 903 leaving Bangkok on May 4th at 8:00 am and arriving in Siam Reap at 9:00 am
OR , for an even later departure (ie it gives more time for the Auckland leg):
Fly Emirates 433 leaving Auckland on May 3rd at 4:55 pm and arriving in Brisbane at 6:35 pm
Fly Thai Airways International 992 leaving Brisbane on May 3rd at 11:59 pm and arriving in Bangkok at 5:59 am
Fly Bangkok Airway 903 leaving Bangkok on May 4th at 8:00 am and arriving in Siam Reap at 9:00 am
These flights give them time to land and get to the Wat by 11:30 am (first known sighting).
There are many other possibilities than these that should be considered:
1. If WRP wanted to find a different route on Friday night, May 2 to separate Phil from the teams and parellel the nonstop flight from AKL to SIN and then connecting to get to BKK by mid-morning, in addition to SQ282/SQ970 2355 0645 AKL SIN there is
AKL HKG NZ39 2330 0645 connecting in Hong Kong with HKG BKK CX713 0855 1035.
May 4 BKK REP PG903 0800 0900 is the connection to Siem Reap for incoming SQ970. Unless CX713 arrives early, connection to PG905 1100 1220 will not be possible and those teams would have to take PG913 0310 0430
2. Why would teams wait until mid-afternoon to start flying north? I can't think of a good reason since they have this combination(note that we are now Saturday May 3 so this causes negatives for normal flight schedules):
AKL SYD LAN801 0525 0705 or QF40 0550 0730 or NZ101 0700 0830
QF81 SYD ADL 0930 1115 continuing on the same flight
QF81 ADL SIN 1220 1830
TG410 SIN BKK 2040 2200
May 4 PG903 BKK REP 0800 0900
3. The early afternoon option of nonstop AKL BKK TG419 is a good one if teams waited that long. Almost equally good is
AKL SYD QF790 1325 1450
SYD BKK QF301 1635 2255
May 4 PG903 BKK REP 0800 0900
Those are the logical possibilities. The reports of a team trailing behind out of New Zealand could mean that some teams went Friday night and at least one on Saturday morning.