Last year my 12YO son played on a 13U Select team (54/80) and for his Junior High varsity team (60/90). The seasons overlap so he was pitching from both distances at the same time. He did not have any trouble adjusting to the difference, other than for his CB. Once he got his CB working at 60', he found it broke too late for 54'. He focused just on his FB/CU and saved his CB for the Jr High games. He eventually worked out a different CB grip that he could command from 54', but didn't really use it that much.
To your question about arm problems, we did not see any. We've kept to a regular routine of long toss, running and icing after pitching, etc. like you should anyway. I agree with the other comments about 54/80 being a good transition size; take advantage of it. If you have an oppty to play 60/90 during fall ball, that's a great way to get adjusted. But, if you or he really want to move up to 60/90 I say go for it. Every kid is different and only you and your son will know for sure if he's having trouble. Good luck either way.