Did they oil the cylinders and redo the compression and leakdown? It could reveal whether it is a ring or a valve issue. Possible it's nothing more than stuck rings and a Seafoam or Yamaha Ring Free enema could fix it. It could take awhile. (Running the snot out of it from time-to-time doesn't hurt either!) AS you are probably aware, 78,000 miles is not a large amount of miles on the FJR motor - unless it has been badly abused. JamesK (above) had well over the 200,000 mark on his original motor and I am closing in on 200,000 as well (next spring maybe).
If the indication is valves, a valve adjustment isn't going to do a thing except put a few hundred bucks in your mechanic's pocket. I have never heard of valve clearance dropping to zero (or negative) which is what would have to happen for clearance to be the issue on a cold motor. Have the valves been checked before? They rarely need much, if any, any adjustment in much under 100,000 miles. Possible that the valves are carboned up and preventing complete closure. Try HaulinAshe's Seafoam treatment (he really does know what he is talking about).
https://www.fjrforum.com/forum//index.php/topic/156782-seafoaming-your-fjr/page-3?do=findComment&comment=1133722
As far as head work or new rings are concerned, be prepared to pay a bunch of money with no guarantee on results. Are you competent to try it yourself? (I'm not)
You would be far better off to pick up a used engine on eBay and swap the motors. If you don't find an AE version, you can use parts from your motor to make one - really just the shift drum, I think.
Edit - a number of them on eBay now for under $900 including one for an AE.
If it isn't something simple like stuck rings or carboned up valves causing the bad compression numbers, it probably ain't worth trying to fix as JamesK suggests above.