Mulch will do what you need it to much more satisfactorily.

At the very least, compost is soil and while putting down a thick layer of soil will smother some of the weedseeds, the new seeds that fly in are going to love all that rich soil. So a mulch will be much more effective, especially if you can find one that is mostly wood chips with little soil, and yes, put down another layer of paper under the new layer of mulch. The fresh paper will do better at blocking the light than plain mulch alone.

You might consider planting the slope thickly with a sturdy (but not overwhelmingly spreading or invasive) ground cover. If close enough together, the leaves of the desired plant will shade the soil to prevent most weed seeds from sprouting. Look around at a bed of daylilies - once established, little, if any, weeding needs to be done... and that is easier than having to re-mulch every year.

Thank you rizho 1 and medly nva for saving me from causing myself more work.

I am hoping that this is the year everything takes off so that this will be one of the last times I need to think about more mulch.

Oh, no... most gardeners never stop thinking about mulch... where to get it, where to put it, and -always- how much more does that bed/bush/slope/garden/etc need...

It's just that on one hand (*after* everything's well-mulched) you can be rather relaxed about it, sauntering around with a cart of shredded leaves; while on the other hand, if you try to ignore it, weeds will manage to poke through in the most awkward spots and you end up having to pull those intruders and *then* mulching.