Question: Doc seemed hell-bent on destroying the DeLorean. So why did he go to the future and get a hover conversion done on the train? Why didn't he just build the train, return to his own time and then destroy the train?
Answer: He didn't return to the Old West, both of them had a desire to go to the final frontier. Their favorite author is Jules Verne, who wrote "From Earth to the Moon."
This is pure speculation, as there is nothing in the movie to support this.
Answer: Doc was happy living in the Old West but returned to the future to collect his dog, Einstein, and he didn't want Marty to worry about him. He probably also wanted to make sure that Marty had made it safely back to his own time, to properly say goodbye, and make sure the DeLorean was never used again. He never indicated he would destroy the train, only the DeLorean. The hover conversion on the train would have been done in the Old West, not in the future.
I doubt he was able to make the train hover in the old west, whilst he could easily go to the future with it and do it there, like he did with the DeLorean. He did say he has been to the future with it, so it's logical to assume that's where he upgraded it.
Doc never says he went further into the future with the train or did the hover conversion there. If he could build a time-traveling locomotive in the 1880s, then he could create a hovering one, as he had the knowledge. Marty asks if he's going back to the future, and Doc says no because he's already been there. That could be interpreted a number of ways. It's a sci-fi movie, and there is a lot of suspension of disbelief employed here.
While the movie isn't explicit about when or where the Time Train was built, other sources do indicate its hoverconversion was done in the future. While Doc could invent a machine that was capable of time travel (the mechanics of which aren't really discussed), he had to travel to the future to convert the DeLorean and couldn't even fix the DeLorean in the past.
What 'other sources' indicate Doc travelled to the future for the hover conversion? Any fan speculation is invalid. I also don't get the argument. While Doc was unable to fix the DeLorean when Marty was in the Old West, he could, and did, in later years, build the time-travel train in the past. He could not otherwise have gone anywhere into the future to do anything. Time-travelling without the hover ability would be extremely difficult as a locomotive would be noticeable and require taking off and landing on empty train tracks. Doc would have to hide the locomotive while converting it. He would also have to know before time-travelling that the railroad tracks he took off on still existed in the future, as he could possibly arrive smashing into what became an urban development. This should be considered as both a deliberate plot hole and a plot device using "suspension of disbelief" solely intended to give the series a spectacular finale.
The comics reveal that Doc Brown traveled to 2017 in a prototype time machine and purchased materials which he brought back with him to the 1890s to use on the Time Train.
Answer: Quite a bit of time has passed for Doc since Marty went back to the future; he and Clara are married and have two children who look between six and ten years old. Plenty of time for him to change his mind and decide he likes the time traveling life with his family.