Besides what are your design choices, this is what I see into industrial drives and photovoltaic inverters.
Hardware current limiting is usually done simply as a protection, with a couple of comparators acting on the switch drivers and input to the microcontroller, while current control is done in digital, like the other loops.
The control update is done at 10-20kHz, which might be too much for an MSP430 (is it really so?), but are easy to achieve with a C2000 or similar. This gives a large freedom in the design and tuning of filters, controllers and so on. 5kHz can be sufficient for a motor control if there is enough inertia and the electrical frequency is not too high.
The real question I wanted to ask you was if the rectifier is a thyristor bridge or a MOS/IGBT one. In the second case, synchronous control would be an option.
Excuse me for the unsolicited info, but this is my research field, and I'm glad to speak about it