It can be recouped. I've had to do this kind of rescue many times. How difficult it will be partly depends on the the kinds of weeds and grasses you have. That is, how many of the weeds are perennial, how deeply the weeds are rooted, how badly the soil is invested with weed seeds, and how much of the grass is runner-type grasses.

It sounds like most of the perennials you want to save are fairly small. If it were me, in the mid-late spring when the perennials are really awake and starting to grow, I would chunk them out and pot them up. Just get a fair amount of soil around them and put the pots in partial shade or shade. The great majority of perennials will tolerate this fine, even for a couple of weeks, at this growing-time of year.

This gives you the chance to weed the bejabbers out of that bed. If there are a lot of free-seeding things like thistles and annual grasses, I would start by scraping away at least the top half inch of soil and dumping it into composting bags for the city to take away.... NY soils should do ok with this, and you will remove most of the seeds they put out last year.

Then weed thoroughly. Get out what you can of the grass runners and weed roots. You won't get them all, but you can beat them waaay back. Then replant the plants, mulch well, and just be vigilant for a while with weeding out new growth.

When you replant the plants, be sure to turn them out of their pots, remove any weeds, and scrape away the top of the soil and shake off loose soil. You don't plant to be planting weeds here.

It sounds like more work than it really is. Don't panic (grin)....