Are you thinking of taking him to 3'6"? Are you planning to jump the daylights out of him? MOST of the time a horse is on course, he is not jumping but working on the flat!
If you can get him trained to meet the jumps right and you are not going to go really high you may be ok. Try it and use boots on him like those professional Choice deals that support the tendons. There may be more modren boots that help more. Also, keep his feet done and correct.
Now, if you are planning on Grand Prix or advanced Cross Country you may want to re-think your plans.
Honestly wish I could see more Cleveland Bays out there working. They are a bit long in the back but really good horses.