Two things to say:
(a) remember, particularly if using preparations containing aminopyralid or clopyralid or similar, that any hay made from sprayed fields could still contain active ingredient, which would remain active on passing through the livestock which eat it and end up on - and killing - your vegetable garden. Always make sure that the manure resulting from the feeding of such treated grass - or from the hay or silage made from it - is put back on grassland and not where you want broadleaved plants to grow.
(b) it's early days, but I can report that we split a field infested with buttercups last year. One half was ploughed, mucked, and turnips and cabbages sown; the other half had the pigs running on it. We had a terrible non-crop of the turnips and cabbages (and no I can't be certain there was no muck from stock fed on hay made from grass which had been Grazon-ed!) but that half of the field is now full of rank grasses, reshes - and buttercups. In fact, it's more-or-less 50% creeping buttercup, just as it was before we started. The pigs' half is of course rather bare still (the pigs are still on it - I said it was early days for reporting!) but there are still docks to be seen (the pigs don't eat all of these, they can be toxic in quantity to pigs) and so far, nothing much in the way of buttercups.
I will report again!