The left cap bank voltage never goes above the right bank voltage, so you don't need a real 4 switch buck-boost, simply a bidirectional buck (it bucks in one direction and boosts in the other).
Here's how I'd do this : build a cheap 10 amp bidirectional current source, and put 10 of them in parallel.
The current source is simple. I have used this to drive LEDs and charge/discharge LiIons and also supercapacitors (much smaller than yours). You got a pair of MOSFETs, a driver (the likes of ADP3120) and a fast comparator with hysteresis whose common mode input includes ground. And of course shielded inductor the size of your thumb.
The comparator is set to control the current, centering it around the target value plus or minus hysteresis. When the inductor current drops below the lower threshold, it turns the top MOS ON. When the current crosses the top threshold, it turns the top MOS OFF and the bottom MOS ON. To change the direction of current or its value, the DC offset added to the comparator input via a few resistors is controlled.
That's it, one channel will set you back about 10 bucks, build 10 and you're done.
Pros :
- divide and conquer approach spreads dissipation, I2R losses etc, so it becomes manageable
- 10 amp module can be built and tested without risk or expensive gear
- blown parts cost $1, not like an IGBT brick
- hysteretic buck is foolproof since it regulates the current
- no risk of inductor saturation, overcurrent, etc
- it is a current source, doesn't care about short circuits, can be paralleled etc
- no need for precision on anything
- frequency self-adjusts, minimizing switching losses ; frequency is easy to calculate depending on in/out voltages
Cons :
- You need to check that the MOS driver can startup with a non-zero output voltage, ADP3120 cannot, some of its cousins from IRF or OnSemi (NCVxxx) can.
That's about it... it just works...