Hi Catherine,
I am a little puzzled by some details here but urge you to pursue your original course.
For example Homeacres was infested with creeping buttercup and ultimately I found it an easy weed to mulch, after some doubts this time last year as new leaves were ominously poking through the mulches. In pathways I re-covered them with more cardboard, in beds with 4-6in of compost on top it was trowel work to remove as much of the new white stems as possible, and they soon gave up, by the end of May, and they are definitely less enduring then dandelion and couch grass.
I cannot see that rotovating will help alleviate compaction, especially if it rains again, you will just have a pudding! also rotovating will not bury the weeds. And your clay is not too compacted or buttercups could not be so strong, I expect it is just dense and full of goodness.
Growing veg in beds where perennial weeds are dying underneath also helps to weaken and shade them.