Epimediums are rather slow and expensive, but quite weed-excluding. Rye and wildflowers usually need Sun.Also expensive, but dense, are the grass-like Carex. Any of the evergreen gingers, Asarum, Hexastylis? like A. europeaum, get very dense, but they are not cheap.
I find the periwinkle and impossible weed, but Pachisandra does not bother me. Proper, Scientific names are escaping me, but Mondo Grass seems weed excluding and permanent.
If you want low, evergreen shrubs, Cephalotaxis Harringtonia comes in a low-growing form, as does Sarcococca humilis.

You probably will need to roto-till and incorporate some leaves, peat or mulch to loosen the soil. The extra effort will bring great rewards and may, actually, be essential to success.

If you didn't already, you might want to have a layer of cardboard or thick newspaper overlapping to smother the weeds. Some of the perennial weeds will still go through, so usually I mow quite closely to the ground or weedeat it bare almost. Grass clippings + browns will compost in place nicely for you. Top with some mulch material for a uniform look. If the mulch is coarse wood chips at least 4" thick you can just leave that and renew yearly or as needed.

Vinca minor will take off, but will need time to fill. Mulch will give you more time to cover ground until then. Marianne Binetti is a NW garden writer who likes easy solutions & has books that can give you more details for what would grow for you.

Does that help?

Some good suggestions given! I really like the Sarcococca for a situation like this but is spreads rather slowly. Great winter scent as well. Vinca is not so much the problem in the PNW as it may be elsewhere but I would avoid planting it near natural areas. In a garden setting, especially a mostly shady one, I find it to be an excellent and manageable groundcover and quite good at weed suppression. The pachy is great as well.

One of my favorites for this situation is Euphorbia robbiae. Evergreen, loves shade, tolerates dry conditions and spreads well. Sometimes too well :-) But easy to remove if it starts to get out of bounds. And I second the mulching after initial planting to help to keep the weeds down. Once the plants root in and start spreading, there is less need to mulch routinely but mulching that first planting will give you a head start on keeping the weeds under control.

I might add that NO groundcover is 100% effective at weed control......the weeds are too clever to be smothered out entirely! But some do work better than others at keeping weeds down, typically those that layer foliage and stems on top of itself - like the vinca - or spread quickly, like the euphorbia.