One thing you will have to worry about is when you close the switch to recharge the cap. I will arc because of the high voltage and there will be a huge current flow. This will probably wear down the switch. You probably need some way to limit the current until the switch is fully closed. Ofcourse adding any number of switches will not help cause the final one will still have the same issue. If you were to add an inductor this would prevent the large instantaneous current but will can cause other problems such as oscillations and slow charging times. Something like a choke might work but not sure. It would need to be chosen so that there is not much overall effect on the charging of the cap except initially when the current is highest.
Although I would imagine that the transformer itself would act as a choke to some degree and you might not have this problem. Maybe the best thing to do would be to experiment and actually see if there is any arcing. I doubt it will be a big issue but could be.
I'm not sure. (still a little unclear on what exactly your trying to do)
What do you mean sync? You mean fire them both at the same time? Do you have more than one? If you just need to pulses of opposite polarity then you don't have to do anything fancy. Just charge the caps up in parallel, disengage them from the circuit using switches. Now you have two caps that are isolated. Now when using them in the discharge side its just a matter of how you hook them up that determines there relative polarity. You can set this up using relays so that it can all be automated.
Suppose for a sec that you could only charge the caps up by "hand". That is, you had a 2000V batter and you connected the caps up to charge them then removed them. Now you have two caps disconnected from any circuitry. Could you then hook them up to your discharge circuit and have it do what you want? If so then notice that you did nothing special in charging the caps w.r.t polarity but just "flipped" them in the discharge circuit. You can effectively do all this with just switches and automate it.
The only draw back to this is that it requires more switches(relays or motorized switches) and is slow compared to charging up the caps with polarity taken into account.
Hopefully that makes some sense. I'm not sure about the transformer though. I would say to go ahead and try it though for the experience as it probably won't hurt anything. (might catch something on fire but thats the fun in learning ;)
Jon