That sounds frustrating. I spend so much time propagating because it is relaxing to me. But there is a lot of internal pressure to pull weeds. I don't mind doing it, except when it's so hot.
If you are considering digging to create new planting areas, consider smothering. So much less effort & the future weeding is much less.
Corrugated cardboard can be the bottom layer, just remove any tape or staples. I love starting a new flower bed with cardboard (covered with mulch, leaves, pine needles, kitchen scraps, yard trimmings - whatever I can find.) IME with doing it a bunch of times, the thickness of the organic matter on top is the key. It needs to be significantly heavy enough to physically prevent growth pushing through. Overlap seams & "patch" any holes or rips with another layer. if you have enough patience and it's not too windy, newspaper can do the same but it takes at least a dozen layers, and is so hard to cover without shifting.
This would not be ready to dig in until spring if started now, but worth doing wherever and if that would fit with your overall goals.
It sounds like you are propagating perennials. If so, maybe you could store some of the plants in your basement instead of trying to get them in the ground? It's about late to do that where you are, if you're not doing it in the next week or two, from what I observed gardening in OH most of my life (moved to AL in 2007.) Rush-jobs where I've hurriedly dug up grass to have new places to plant stuff has hardly ever gone well for me, here or there.
There's also an option of over-cramming, depending on your current spacing of existing plants. While you work @ new areas, you could cram plants into existing areas until you have more room to spread them out more.
Another option is to pile the pots up against a shed, or just somewhere in the yard, and cover them with a big pile of leaves.
