We're moving into hazy-memory territory here...
The Kilmarnock does have a relatively weak root system but from what I remember it is the scion (the grafted top part) that keeps this in check. Once this is removed the tree becomes whatever variety the rootstock is and that's when problems can occur. With any tree where there might be an issue with vigorous roots then root pruning is an option worth considering.
My guess regarding the soil is that the willow will not like it at all unless there is a water supply it can readily tap into (pipe/water table) and will sulk, be prone to disease and liable to blow over if allowed to grow to any decent size. Hopefully, someone with more experience of this type of soil will be able to give you a definitive answer (Northants is mainly clay so my experience is limited).
So, what to do? Give it a try - anything has got to be better than having a Kilmarnock Willow
p.s. Can sympathise with you on couch grass.