Sounds like it should work well for a 650b conversion as long as the BB isn't too low.
That said, I used a Cross Check as my brevet bike for a couple of years and eventually got rid of it. I haven't missed it a bit. Cross Checks are good versatile, no-nonsense bikes, but for randonneuring I prefer something lighter and more comfortable riding. Riding a Cross Check for long distance is a bit like doing a cross country road trip in a monster truck. It works, but there are many other rides that will be more comfortable and a lot more efficient.
If you really have your heart set on a 650b bike with GB Hetres, then I understand the appeal of the Straggler as there aren't many (any?) alternatives at that price point. Still, for not too much more money you can get something that should offer much better performance and comfort. Consider the Boulder All-road, Ocean Air Rambler, Rawland Stag, Soma Grand Randonneur (when it ships). I'm sure there are others I'm forgetting.