There are similar programs to an MSTP for fellows and faculty, but the better question is why? The T32 will offer you a truncated version of the same thing and can be done within the context of your clinical training. Yes, it is less structured, ie there typically aren't formal didactics. There is still some version off a committee though. The requirements of a T32 really aren't a stringent as a formal Ph.D., but the only thing, at your juncture, that the Ph.D. offers you more time. Mentor ship is always is a crapshoot, irrespective of the degree or training you hope to obtain. However, it also does it at a significant cost (ie who is going to pay for it?). You may be able to swing some clinical time, but not enough to pay for your Ph.D.. Thus you would have spent all of medical school and residency to pay for something that you could have gotten for "free" a decade prior. That doesn't make much financial sense.
Your best options at this point are T32 (or F if you can swing it during fellowship), then K, then R... and so forth. You're too far along to pursue a Ph.D. in my opinion unless you 1) have less interest in any sort of clinical medicine 2) are willing to accept the financial costs associated with it (and you much be willing to accept 1 and 2).