I personally think that the main distinction between positivists and interpretivists and pragmatists is in the varying kinds of confusion they are subject to. Unless you're a full-blown relativist, the endeavor is the same, the methods are the same, the goals are the same.
What is a qualitative interview yielding understanding other than an observation and measurement computed in the head of the interviewer? All you can manage by rejecting the positivist aspect of interpretation is to embrace being confused and misled. It's perfectly okay to say: human subjective interpretation is the best measurement tool we have for this. To say, you can't measure this and yet I'm going to come up with the right answer in some sense is just wishful thinking or confusion about what one is actually doing. So I don't think there's actually much of a logical gulf between those approaches done well. (For instance: a good interpretive study would try to estimate measurement error. You always want to know how good your measurements are, even if the measuring device is a graduate student chatting with someone.)
Pragmatism again is in accord but focused on a different aspect of a problem. All models are incomplete, which is to say wrong in some sense. Why bother with wrong-in-some-sense models at all, except if they're useful in some way (at least useful for appealing to your sense of elegance or completeness!)? One can argue about which aspect of utility is most important: I-can-predict-something-a-bit-better-now vs. this-is-reliable-knowledge-that-we-can-write-in-textbooks-and-trust, for instance. But to the extent that pragmatists say anything new, it's only to the extent that others have gotten confused about the nature and scope of what they're doing. Otherwise, it's just a difference in degree, not kind, as the pragmatist would probably be better disposed to useful-now theories than a self-identified positivist.