I don't recall seeing any ICs past 600-700V (you
can look at Power Integrations, IXYS, etc.). My off
the cuff suggestion is for a push-pull scheme where
transformer can do the down conversion, and some
power switch like IGBT (low freq high current) or SiC
(see 1600V power devices now, push-pull uses low
side FETs only on the primary which is good since SiC
gate voltage requirements are unhelpful and flying
high side drivers, few).
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There are some outfits that do HV modules but I only
recall seeing them go the other way (5-12V to kV).
Still maybe Pico has something for you.
Cheap, and kV, however do not usually go together.