I'll leave the semi-conductor circuitry to the experts on this topic. I'm just a hobbyist in electronics and this is way out of my hobbyist league. I can suggest an alternative device you may want to consider. If nothing else, perhaps it may encourage you to contact a few companies providing such devices and have a conversation with them about existing products that may fit your application area.
So below will be a general discussion of the idea. (I know that commercial gas discharge products today can handle upwards of \$20\:\textrm{kA}\$.) These products are especially indicated when you are talking about fast and high current and high voltage. So that is why I'm bringing this up.
Like everything, physics matters. A triggering delay may be very predictable (the hot-cathode with priming electrode comes to mind) or it can be a bit variable. Also, the speed of the discharge can be fast (several design parameters involved here) or it can be slower (long, narrow tube with outside metal band as an electrode, requiring the discharge to spread throughout a long, narrow tube.) So it's important that you know exactly what you need here: trigger delay time, trigger delay predictability, allowable pulse duration, etc.
A thyratron is a gas discharge tube that can be triggered. The solid state equivalent is, of course, the thyristor (SCR, et al.) The reason this came immediately to mind is because physicists have been researching high current, high voltage pulses for quite some time. A lot has been published since about 1950, or so. These were (I can't speak to now) particularly used when there was a need for extremely precise, repeatable, and narrow triggering pulses (such as was required for so-called "nuclear triggers" used with early plutonium bombs, for example.) So lots of money spent here, of course.
The physics of gas discharge requires at least 2 spatial and one time dimension of PDEs coupled to at least 6-dim ODEs to apprehend well. (That doesn't include radiation transport and atomic interactions.) A simpler version will use global rate equations that assume spatially averaged densities for the charged particles and neutral atoms and molecules, but then it still needs to deal with excited and metastable states. There is a modest, intermediate text by Lieberman and Lichtenberg called "Principles of Plasma Discharges and Materials Processing." (From John Wiley and Sons.) It has a good treatment on the fundamentals of discharges and those simplified global rate models I mentioned, plus something on collisions and DC and RF discharges.
Thyratrons in both cold- and hot- cathode varieties. They are still quite important; most especially whenever you see the combination of two or more of: (a) high-voltage; and, (b) high current; and, (c) fast-switching. Your application seems almost an obvious fit to me.
With cold-cathode thyratrons, you apply a voltage above their extinction voltage but below their strike voltage. In your case, you'd need to find one where \$1000\:\textrm{V}\$ is bracketed by the extinction and strike voltages. (They can easily be designed for such a voltage, if you can consider getting one designed.) Once that voltage is applied (easy for your case), a pulse is then applied to a trigger electrode that causes some local ionization which will then spread throughout the tube quite quickly.
A hot-cathode thyratron is a triode (but with substantial gas) where a negative grid bias is what holds them off from triggering. These may include a priming electrode to increase the speed of the trigger and to make for more robust and predictable triggering parameters, as well.
Triggering electrodes can be inside or outside the tube. The typical camera flash will use a small band of metal around the outside of the tube, for example. (Those are usually high-pressure Xenon tubes.)
There is no reason I can think of that you cannot make all this work with semiconductor devices. Your current requirements are within reach; your timing is within reach; your voltage requirements are within reach. If treated individually. But there are parasitics involved and your requirements may dig pretty deeply into the physics of semiconductor devices.
So I just wanted to offer an alternative area to check on, as well, since you opened the doors.