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+1 on rico's comment about small thyristor flashes.
Use a smaller light, placed close.
Small flashes, like the Canon 580ex, are _much_ faster than studio lights. The lower the power setting on a 580ex, the shorter the flash duration. (This is the reverse of a lot of studio lights, where duration is inversely proportional to the power setting.)
A 580ex is on the order of 1/833 second at full power, but around 1/15,000 second at 1/16 power. It's even shorter at 1/128 power, maybe 1/35,000 second.
If you need more power, and you want to use your Elinchrom accessories, you can always buy an older (analog) Elinchrom EL250 (standard duration) or an EL250R sports ("rapid") monolight. They're pretty common used. The EL250 was about 1/3600 @ t.5 and the EL250R was around 1/6000 (when both units were set to full power at 250 w-s). Unfortunately, the EL250 and EL250R had their shortest duration at full power, unlike Canon speedlights which get faster when power is reduced.