> ? or does it place it elsewhere, say, in the will

NO!  Wittgenstein, Whitehead and other process-oriented strategies surely do not put the foundation in the will.  Everything is one big feedback loop, and choices are part of the loop.  Will can have application only given meaningful things to want, meaning is dependent upon usage, and usage is dependent upon the composite of all the moves people make, which may express their will, but, as noted, that will can act only based upon meaning.

> Seems to me that rather than really get rid of foundationalism pragmatism says the foundation is what we choose (deliberately or otherwise) to do. 

That is looking at one part of the loop as the basis.  A feedback loop has no most important or most stable part.  So this is really a non-well-founded structure.  Imagining that there must be a foundation, you can claim they have given you one.  But you are projecting your viewpoint onto them.

Yes, there is no foundation to a foundationless structure.  This is not a paradox, it is a definition.  If you have a problem with it, deal with the insufficiencies of some foundational system and elevate it into a foundation.  Unfortunately, folks have been trying that forever, and Quine kind of proves this just can't happen.

> To revise our theories requires in some sense a deficiency in our theories. And to sense a deficiency requires a sense of what should be but is not. 

You vastly overstate what is lost by letting go of a foundation.  All that is left is not the surface.  By definition that is the surface of something, and that thing is deep and has a lot of ballast that keeps it from shifting around too much.  We can note deficiencies not by looking at some ultimate source of truth, but by looking at how things are sometimes easier and sometimes harder, and making moves toward getting rid of the hard parts.

If any individual or collective will got to choose the definition of 'harder', we would indeed have a foundation.  But we don't.  There is not a collective will, or we would not witness constant contests of will.  And since we are all involved in the movement, no one of us is in charge.  As Whitehead points out, you can personify the amalgamation of will and define it as God, if you really want to, in which case, yes, God is in charge and He determines everything.  But this is not a very useful God, and he remains wholly optional.

> And in just giving, everything becomes necessary. 

Nor is there any logic behind the notion that without a definition of necessity, everything is necessary.  It is like saying without a definition of blue, everything is blue.  Anything might be necessary or it might not be.  By 'just giving' we accept reality and do not pretend it has to be shaped by some particular force which we can call 'necessity'.  Which is what we intended to do.

> Yet, in what other way can mind-independent reality interact or influence the autonomous rational will?

There is no mind-independent reality and the rational will is not autonomous, they are locked in a feedback loop.  Assuming the two things you have inappropriately insisted pragmatists believe bars an answer.  Given that, your question comes down to 'Assuming the impossibility of stability without a foundation, how do we ignore that possibility completely.'