Turns out the engine stopping after putting in gear was an issue with the seat switch.
I've been trying to fix engine stalling and rough running under load for about a year. I changed fuel filters (both) for I think the third time in six months and the tractor is purring like a kitten. I have been told that the filter design and filter quality is poor, so I guess this proves the point. If you have a rough running, low power under load condition, it might be worth replacing fuel filters even when it doesn't seem warranted.