John Deere 420 (1950's) Starting Problems

I have an old John Deere 420, built in the late 50?s. It has a 6 volt system, positive ground. For the past several years it has been very slow to turn over, especially after it has ran for good while. I bought a new battery last year, hoping that was it, but that did not help. It was warm all last week so I decided to start it and service everything yesterday for the first time this year. I pull the battery in the winter, so on Friday I charged the battery that I had bought last year. I had gone to Tractor Supply last week and bought two new battery cables, 14 inch 1 gauge. I took a drill and steel brush and brushed the ground down to bare shiny metal. I also brushed the starter post down to shiny metal. Once everything was connected, I turned on the key and pulled the starter, it turned over quickly and started right off. Tractor ran great. After running it for thirty minutes or so, I turned it off and tried to restart. It turned over very slowly about three times, I stopped and waited a few seconds and tried again. It still turned over slowly, but it did start. Once it started it ran great, but I was afraid to shut it off again. I decided to start it again this morning to see if it again started quickly on the first try. It was about 55 this morning and when I attempted to start, it turned over very slowly about three times and then stopped turning over. I waited a few seconds and tried again. Once more it turned very slowly but did start. This has been the pattern for perhaps the last three years or so. I was hoping the new battery and new heavy cables would take care of the problem, but not so. Any suggestions? Should I pull the starter and have it checked out? Thanks for any advice you can offer.

What you have done so far sounds good to me.

A next step you can take is to remove the switch from the starter and see if the contact buttons are badly burned.
Some filing on them will help.

But if that starter has never been off the tractor, you're overdue to have it worked on.

Thanks jCarroll, I think I'll take the starter off this week and take it to have it looked at. I appreciate the advice.