I had planned to do that last fall, but found the growth to be too green and tough for me to cut easily. So I am cutting and pulling it by hand now. There is lots of bare soil as well as emerging multiflora rose and creeping euonymus (which chokes the trees). Would it help if I sowed grass seed, planted daylilies or pachysandra? The slope is east facing, with some old apple trees in need of rejuvenation, tall maples and hemlocks.

Maybe you need a brush cutter rather than a string trimmer. And it needs to be done as soon as the daffs have died down. That would be late May here. If you wait until the Autumn your weeds will have had en entire summer to get away from you. And you might need to cut it a couple more times before the winter. I don't think there is any point trying to grow any thing else there until you are on top of the weeds, especially the woody ones.

Can you show a picture of the area?

It is much later than May by the time daffodil foliage turns brown here outside NY.. But you are so right that I should time the cutting as soon as it happens rather than wait til fall. I don't know if I'm strong enough to wield a brush cutter. I think they are all gas powered, no? I will post a picture as soon as I clear the debris of apple tree trimmings I created today.

The RHS did a study which found that the foliage only needs 6 weeks before it can be cut down without detriment to the bulbs. It doesn't need to be entirely dead.

OK, then you have given me a game plan. Six weeks after bloom (which will be mid-june here), whack all growth, then monitor the weed regrowth to determine next step.

Just remember, Nature abhors a void...until you get a cover crop in that's growing strongly, whatever is in your seed bank and/or environment (read bird pooh) will keep trying to come up and fill your void. So in my assessment, I'd rescue the daffodils and plant them where you can control them.

Otherwise, figure out what you're planting there (that can compete)...and while it's "boring", a daffodils do seem to thrive in places there are no longer evidence of houses...right through the grass. But...without some form of control, grass is likely to be displaced by taller perennial vegetation (vines, trees, shrubs)...so maybe graze cows on it (lol).

I don't know...it sounds a mess to me...

So I should at least toss grass seed down now?

Kitasel I am in TX and I did prepare my daff area by clearing weeds and mulching for future weed prevention. Weeds still reared their ugly head so don't feel bad. Like you, I do some manual removing but mostly grin and bear it til daff foliage is yellow and we can mowe. The bright side is that as daff clump expands it seems to suppress weeds.

Borrow a small hand lawnmower and run it over the area after the daffodils bloom.

You could cover the area with a tarp to "starve out" the weeds after the daffodils bloom. You could mulch the area with a thick coating of mulch.

You could plant it with bee balm.

If this is a slope and you somehow managed to keep anything other then daffodils from growing there...you would probably end up with erosion.

Bee balm! OK, I have my first suggestion for something to plant to hold its own with the daffodils and the weeds. I should say that "weeds" that are meadowlike and easily cut once a year are not the problem. It's the invasive euonymus (wintercreeper) and brambles that are the real headache. If there is a way to keep the wintercreeper under control (in bounds and off trees and shrubs) I could even live with it.

'Borrow a small hand lawnmower and run it over the area after the daffodils bloom.'

A picture would be really useful but from what kitasei says there is Rosa multiflora and Eunymous which a mower wouldn't be able to tackle.

Yes, I find the euonymous impervious to weed whackers as well. It lays too flat. I should learn to wield a machete..

And if the slope is too steep, it would be hard to get the lawnmower to go up it.

A Brush Hog would work, but would be expensive, and might damage the bubs.

Someone online suggested a Weed Wrench for burning bush.

Standard way to keep vines from climbing your trees is to cut them near the base of the tree and paint the cut with Round Up. Harder to do with shrubs.

Echinacea ia another cheap, pretty but aggressive native you could plant the area with.

How large is the slope? I'd be inclined to tackle this with multiple strategies. I would mow/weed whack once or twice a year, late spring and fall. This will remove any new woody sprouts and prevent the invasives going to seed. If you can find time once or twice a week, go out for an hour or two and cut back to the ground the woody plants, then paint the top surface around the outside (just inside where the bark is) with an herbicide such as undiluted glysophate to discourage regrowth. You don't have to do the whole thing at once, just pick away at it. It may take a couple of years, but this will eventually get things under control where just the mowing/weed whacking should control almost everything. If you want a wilder set of flowering plants let the current wild plants grow and add vigorous growers/self seeders that are suited to your area and soil. Rudbeckia 'Goldsturm', beebalm, obedient plant, gooseneck loosestrife, Lobelia siphilatica, Joe Pye weed, Queen Anne's lace, catmint/Nepeta, goldenrod, asters, Oenothera fruticosa (sundrops evening primrose) and valerian are some plants that will seed around with abandon or spread via rhizomes and all have at least some reputation as garden thugs, exactly what you would want here. There are several perennial Geraniums that could work well, including G. sanguineum, G. maculatum, G. maccrorrhizum or one of the G. cantabrigiense such as Biokovo.

If you want it to look more garden-like, mulch heavily (several inches) and then pull aside the mulch to plant. Then let things seed, but get to know weed seedlings vs. desired seedlings and do selective weeding a few times a year.

This is very helpful. Can I ask you to recommend a few plants for the shaded areas, those under hemlocks and maples, and the old apple trees?