You don't say where you live but in my part of the U.K. at this time of year D3200 is fine in both daylight and relative darkness but given this isn't the case for you then you have two options:
1. Use ND or B&W filters such as an orange, green or red
2. Swop films as you have mentioned
Well there may be a third option which gives some flexibility but yes it does involve a 400 film. My very short experience with TMax 400 is that you can switch between 400 and 800 and develop for 800. This still might mean a filter during the day but you might get away with a yellow which alters the negs less but of course 800 needs to be fast enough.
Based on your examples this would give 1/30 at f2 which might be enough. Incidentally you could go to f11 and 1/1000. OK the DoF is greater than f8 but is this a problem? I assume that 1/2000 is only a problem because you don't have this as a shutter speed?
There isn't anything wrong with fast shutter speeds per se if the camera supports these
Finally just remember that B&W has a great range so I would think that overexposure by rating at 200 if this is necessary during the day and developing for 400 but exposing at 800 should be OK. You can compensate with good old VC paper