buttercups

I just spent the morning removing buttercups from a small native plant garden that I planted last year. I assume this buttercup is lesser celandine. Is this a hopeless task? Each plant had tiny bulbils attached. I couldn't possibly have got them all. Would it be better to lift the natives, pot them up and do what to this area? I prefer not using pestcides. .
Pixie

Lift the natives and solarize by staking down sheets of plastic. I've used tarps from the dollar stores. You could smother too. Look for old carpeting tossed at the curbs. It won't look all that great for a while but it would work and you'd avoid having to use an herbicide.

Equilibrium,
Will twenty layers of newspaper or cardboard work just as well? Or is solarization better?
Pixie

The plastic will work in this situation. I would let the plastic stay put until fall. Let the sun nuke those. Come time to lift up the plastic, I'd put down about 15 layers of newspaper. Cut holes in the newspaper and plant what you want. The newspaper will knock out a little competition and deter opportunists from taking root until you can figure out all that you want to plant back in that area.

Thanks for the suggestions Equilibrium I'm just waiting to see what else comes up before I put down the plastic.
Pixie