I have a very large Gleditisia tree which has become invasive in my small garden tree surgeon has said it is diseased and need to be removed

If you have paid a qualified tree surgeon to inspect it and he says it needs to go, I'd go with what he says, if he's reputable. If you;re not sure he is reputable, go out and push hard on the trunk of the tree to see how stable it is, inspect it from the bottom upwards for signs of disease (soft, sunken areas, missing bark, anything that doesn't look healthy); also ask the tree surgeon precisely what he means by 'diseased'... From your description of its growth pattern in recent years, it certainly doesn't sound like its healthy.

welcome to GoY.
I agree with Bamboo. if the tree surgeon is reputable why would you not take the advice?

You could always get the advice of another specialist before making the decision.