put out a sucker below the graft

We tell the trees to grow, and they do grow, but just to spite us. (That's called "malicious compliance.")

(non-native) purslane species

I don't think that it matters at this point. Native or not, it really is a useful plant, not only for the garden, but also for those sidewalk cracks where nothing else seems to grow.

I’d be worried about runoff.

You'd only need to prevent the water from spreading it around until it breaks down. If you compost it on a small raised platform with a roof over it, you shouldn't have much issue. For any minor spillage, you can plant something around the compost platform to absorb it. Once the compost breaks down, runoff would be a concern only due to the loss of hard-earned nutrients, which you could also reduce with vegetation and mulch.

I’d also like to do some cover crops and chop-and-drop this fall for mulch.

I've heard that buckwheat can work as a winter cover crop, though I've never actually seen it done. Do you have any Acer negundo popping up? That would probably be choppable and droppable, though more suitable as mulch for the fruit trees than the garden beds. If you have any Elaeagnus umbellata in your area, you could cut it down for woody mulch as well, but I don't recommend planting it. For mulching the garden beds, some large herbaceous plant probably makes more sense, but I don't know the cold-climate equivalent of banana, and the closest things to Tithonia diversifolia probably wouldn't grow back very well. I do NOT recommend grass.

As an honourable mention... Robinia pseudoacacia is another potential source of woody mulch, but it's probably the nuclear option. I don't know if there are any cow pastures or old copper mines near you, but if so, then this could probably reforest them if you let it grow up to produce seeds. The neighbour's lawn wouldn't stand a chance. If it isn't already growing in your area, exercise extreme caution. This plant is not a toy.