I agree - reflux is painful and one of the main symptoms in babies is arching of the back, my friends baby had it undiagnosed for 8 months and once she was having treatment for it - it was like she had a new baby. The poor thing must have been in such pain and her Mum felt awful that it wasn't diagnosed sooner but it was no fault of hers, I would definately recommend he is tested for it. You sound like a wonderful child carer!
those are the classic symptoms of reflux. Do you know if he does the same thing at home? If so, you may want to suggest they read up on it or bring it to the attention of the pediatrician. Not all babies with reflux spit up. My little one had silent reflux, and she would swallow everything that came up back down (so it burned in both directions). If he is already on meds, they may need to be adjusted. There are many different things you can try to help a baby with reflux in regards to feeding, sleeping, and positioning, but those generally pertain to younger babies. If his symptoms continued to this age, then it most likely he would need to be seen by a gastro, or at least need meds from a ped.
If the baby does not do the same behaviors at home, then it may be that he misses his parents. I would try distraction like margy suggested, and start tracking his patterns. Are there certain activities he prefers, or certain times of day that are better or worse? How long have you been caring for him? Does he cry immediately upon seeing you (separation anxiety)?
I she tied in that he arches like that , a car seat or a high chair ? Have you tried distraction when a child is crying un controllably there's usually something wrong ...Is he like this with his parents have you discussed the issue with them ?