If you have two capacitors, then it would be good to have a separate voltage regulator for each one. Tiggering two pulses in sequence is pretty easy.
The voltage regulators would need to handle the desired charging current, so say 20 amps. A linear regulator is the simplest, but would have to throw off tons of heat. A switching regulator is going to take some expensive parts and add lots of complexity to the circuit.
The switching power supply already has a regulator, so to me it would be much easier to just hack that one rather than build another one to add onto the output.
All switching power supplies have some kind of regulator circuit that could be tapped into to reduce the output voltage. Basically just add a pot to it somewhere. Most of them have built in current limiting too, so you can just hook it up straight to the capacitor (some inductance in the circuit would be good to make the contacts live longer).
For a dual pulse unit, just get another surplus power supply. I think the initial pulse is smaller, so perhaps a smaller supply would do.
Using a surplus SCR to discharge it, there would be no easy way to control the pulse width other than by what voltage you start at. Once those babys turn on, they don't want to turn off.
There is a way to commutate them with another SCR and a bunch of other parts, but it gets real complicated.
I could attempt a drawing of the triggering circuit, but that will have to wait. I need new drawing software (old stuff is not compatible with Vista)

I have other computers that actually work.