The Bridge design is basically sound and boost arc to overcome gap or fluid pressure rise in breakdown voltage is a bonus. The higher voltage guarantees triggering of the power arc that follows and does not need to be high current, it can be milliamps compared to Amps of the low voltage . Each discharge energy pulse is directly related to the CV^2, so it would be useful to have a linear control proportional to V^2 with ranges controlled by switchable C values for different metals, where the energy is measured in Joules or Watt-seconds. Now both the Cap and arc will have low ESR and it is recommended to have the Cap ESR much lower than the Arc unless there is a reason to limit current with lossy ESR, but preferable series inductance and pulse width can control current better with lower loss.
I don't have any EDM experience, but it wouldn't take me long to get up to speed. ( although I have diffusion bonding experience for bonding tubes with radial diffusion bonding up 100kA which is more difficult as the diffusion weld goes around the circumference, the welded resistance naturally drops so more power must rise rapidly from start to finish around the circumference of the tubes joined to maintain constant arc temperature.. ( Zirc. shim for Monel Steel tubing for Nuclear reactors, circa '79)
Perhaps with your practical experience ,we can put together a general design spec in a table of values, from which I could generate a feasible design.
1) Joule range; Arc trigger voltage
2) Pulse width range;
2a) cutoff criteria (Joules or Amps, threshold )
3) Pulse Interval range;
4) Materials: brass, steel , alum , copper, SS , tool steel, molyb. etc. variations...
5) EDM methods; RAM, Small Hole, Wire
6) Fluid types;
7) Fluid pressure ;
8) Electrode material, shape , diameter:
9) Electrode Fluid tube design; single hollow tube, tri-tube in 1
10) ??
This may exist already in a concise EDM manual, but items 4+ affect items 1~3 which I can easily design, once defined.
Most of challenges are in the magnetics as in Welders etc and a non-saturated core is critical, which may be a large gapped core, or non-ferrous core
I would choose battery power with a charger to avoid the line pulse currents that will be 10x the average current of a standard line bridge rectifier with 10% ripple.
When I get a chance, I'll read Anadian's thesis.