If you are using standard white LEDs (I’d be tempted to start from a 5 or 9 led ebay type battery flashlight to get the leds a case and reflector to get a directed beam that may be bright enough) you should (note the weasel word 
) be able to get more brightness by increasing the voltage driving the LEDs to source more than their rated current with a short on long off cycle. Light output is linear with current (but at some current point the internal bonds may melt) and the short duty cycle keeps the heat (which is usually the real limiting factor) within bounds. The newer multi watt white leds I think use a phosfor to adjust the light output spectrum and thus may not turn off fast enough to do what you need (simulate the bright fast output of a strobe tube), but I think the standard 5mm type white leds that come directly from the die should probably work. You may need to drive it from a power MOSFET to get the current you need though.
As well I assume you have seen
https://www.xenonflashtubes.com/
who seem to have cheapish ($5 US or so) tubes although shipping may be a killer.
Peter