I tend to think that Heidegger (early, anyway) may be closer to W and Gadamer on the flexibility of background practices than you suggest. This was a claim in my diss (that he’s closer to G). The basis of my argument turns on authenticity. Ted frequently pointed out that Heidegger is clear that an authentic Dasein’s world need not change. But I believe an interpretation that couples sections 61-63 with chapter 5 yields a position in which the tradition which we inherit can be modified by us. The specific direction such modification takes is, of course, not directly guided by the subject — it happens, as you say about W and G, in the absence of rules or princples. I think Heidegger’s account of fate, in other words, is one in which Dasein is a full participant. And only authentic Dasein, as Heidegger stresses, actually has a fate.
As I interpret Heidegger, things stand in unambiguous relations to one another and goals. Using Ted’s concept of the signifying chain, it seems that the chains indicate actions as the only thing it makes sense to do somewhere. Or that there is a clear line between it making sense to do one thing rather than another. The bedroom as a site of activity may indicate a multitude of actions but these chains aren’t intermingled and confused. They are definite and already in place. I think Wittgenstein, on the other hand, allows for the development of new meanings within such sites and for the fact of ambiguity and polysemic relations. I think there is a clear comparison here between W and Gadamer. In Truth and Method Gadamer comes awfully close to saying that meaning is use in the section on application. But, the implication of this is that there is no rule or universal standing over language governing it. It develops in the very process of being used. This is “meaning finitism.” So ultimately, my contention is that we have overlapping, but often different background understandings of the situations we share (of course we only share them insofar as our understandings overlap to some degree). Again I see W and Gadamer as very close here.