Ground covers that are vigorous yet still controllable, ideas?

I have been fighting a seemingly losing battle against grass. Part of my problem is the time I have available to work on my garden. I am a complete believer in compost, but as soon as I think this first section is good and focus on section two, section one is overtaken with grass again. I have comfrey, which I would edge my beds with, but it takes the comfrey about three years to get thick enough to crowd out the grass. Sheet mulching with cardboard will earn me about one additional year, even with topping up the mulch in the fall.  What I imagine is a ground cover which I can plant immediately after mulching which will hold the ground, and I can then plant trees, shrubs, and annual veggies.

So, requirements are, hopefully perennial, hardy to -30F, vigorous as described earlier but not invasive, full sun, and ideally also productive in some way.

Am I asking too much? Or do I just need to double down on the mulching regimen?

Try white clover, it will get thick enough to out compete the grass. It’s also a nitrogen fixer.

To keep grass from taking over the mulch would need to be at loeast 6" thick though 12" deep is better.

grass is bad because some run underground.  If the grass cannot see light it will not come up.