As to creeping buttercup, it is a great pain for these reasons: in my garden in southern state of Victoria, Australia it kills or suppresses all other plants very quickly and spreads by both seed and runners above and below ground. I have had a long running battle with it and I would not suggest trying to live with it unless you don't don't want any other plants to grow.
My best efforts are: digging it out by the roots especially in spring when the mild frost we get here has beaten it back and it is just putting out relatively short plants. This is absolutely necessary if it has made itself comfortable in the midst of other plants i.e. grown into and among the roots of roses, etc. Also in the cracks of paving stones and bricks. No other way except spray for these guys.
If it has situated itself on flat patches of land you can cover it with lots of cardboard with no cracks for it to find light and then a heavy layer of mulch to keep the cardboard in place - I use sugar cane mulch but probably an Australian thing - it does not move with the wind or degrade very quickly. Organic is best, when you can get it.
Or you can use black plastic held in place with bricks, not my favourite choice but when I have some lying around I will do this.
THEN - leave it in the hot sun of a whole summer and when you uncover it, it should be dead and gone. But do not become complacent, it will come back and it is important to keep digging it out as it reasserts itself.
Interesting to note, the one plant I have found that really suppresses it where you have initially removed it as best you can by digging out as much of the roots as you can or baked it as described above is symphytum officinale - true comfrey. It really suppresses it in a quite extraordinary way but I know it can be somewhat invasive as well. I have also experimented with a few other types of daintier comfrey plants but they are no match for this invasive buttercup.
It definitely thrives in our quite acid soil and I intend to experiment with broadcasting lime where it is really thick.
On a visit to the Zurich area of Switzerland, all the hydrangeas I saw were a luscious shade of deep rose. In my valley I have never seen flowers like that as all the hydrangeas in my garden and valley which are not white are a gorgeous deep shade of blue, with no effort on my part. The colour of hydrangeas are a reflection of the PH of the soil. I noticed the dreaded buttercup living happily and modestly among other plants in the meadows near Zurich. Just a little yellow buttercup nodding in the breeze, not a whole field entirely overtaken by them as you find around here.
Hope this helps and I urge you not to take any advice to live with it. I see Skandi Rogers has come to exactly the same conclusions as I have. You don't have to attack all areas at once, if you have a lot - just do what you can and you will eventually get on top of it. In the meanwhile, keep the untreated areas mowed very short. I would advise taking action on it immediately before you worry about grass. This is a long term project but worth stopping it before it takes over your entire large yard as it did in mine. Not a weed to try to live with.
