Coming from the North of Thailand, speak Chiang Mai or Chiang Rai area or the like, you could take a Rayong bound bus and get off at Prachinburi. You would be there early in the morning. Take the next bus in the direction Aran, Kabinburi and on to Poi Pet. The train arrives rather late in the morning at Prachinburi for your purposes.
At Poipet, buses leave for Battambang regularly. At least one 3-3.30 PM departure. No need for a shared-ride Toyota.
Scenic: North to Korat or, better, Buriram. Then the bus to Aran. Lots of temples along that route.
More demanding: Bus to Surin. Van to the border. On with motorbike taxis to Bantey Chmar temple, on to Sisophon and Battambang. Only with light luggage though.
You could also take the Chantaburi bus from Aran and take the Pailin border as long as you do not need to use an electronic visa. You would avoid the zoo at Poipet although this has been less worse than in years before.