32RH 67 Dart

The 42RH is a completely different animal from OP's 32RH. 42RHs are an overdrive with lockup and require some rather involved surgery on the trans crossmember for the OD unit to clear on an A body; an A999/32RH is a standard 3 speed with lockup convertor that requires little to no mods for installation in an A body, depending on year of the car and year/model of the transmission.
Will the V6 torque converter work behind a 400hp 360 magnum?
The V6 torque convertor will physically work with a 5.9 Magnum, the stall may or may not be optimal for your setup, but it's not too bad. The A999/32RH has a deeper 1st gear that helps. The Factory Service Manual lists the lockup convertor stall speeds as being 1800-2100 RPM for the V6 convertor and 1700-2000 RPM for the V8 units.
To use behind a 5.9 Mag, you need to use the factory Magnum flexplate with the 5.9 balance weights, one hole in the flexplate will need to be ovaled out with a rat tail file or a Dremel- 5 minute job. The 3.9 is internally balanced, so you need the 5.9 external balance flexplate to keep things copacetic.


Recommended kit to control TCC?
No "kit" required, A999/32RH is hydraulically controlled lockup. The only thing you may need is a toggle switch, which I'll get into in a moment.
First, you need to identify which transmission you actually have- while they're functionally identical and people tend to lump them together (even some reference sources tend to use the designations interchangeably), the A999 and 32RH do have some physical differences and are more than just a change in designations, with the 32RH being an evolution of the A999.
(Pictures stolen from JoePole and Cleland)
The A999 has a "smooth" tailshaft housing and no electrical plugs.
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Now compare that to the 32RH. Outward differences are the additional stiffening ribs on the tailshaft housing, and the addition of an electrical connector. used for the Tow/Haul bypass switch on trucks and vans.
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A simple toggle switch to a 12v source (although not required) will allow you to enable/disable the lockup feature on the 32 RH, and nothing at all needed with an A999 since both are completely hydraulically controlled.

*On a side note (not relevant to the OP's original question, but I'm including it here for future generations), if you're swapping one of these into an early A ('66 and earlier) get the A999 since the additional reinforcing ribs on the 32RH tailshaft housing will interfere with the transmission crossmember and will require extensive grinding to remove much of the ribs. Not an issue with the A999. On '67 and later A bodies the 32RH fits fine.