According to the sunny f/16 rule, you could move your shutter speed to 1/8000 and just need 1 stop (0.3 reduction) - see below. You could also consider a variable ND filter since this calculation would not account for the additional light your strobe would provide. You may want to consider shooting in open shade or using a scrim to reduce the light.
Sunny f/16 = f/16 ISO 100 S/S – 125
f/16 – f/11, f/8, f/5.6, f/4, f/2,8, f/2, f/1.4 = 7 stops
S/S 1/125 – 1/250, 1/500, 1/1000, 1/2000, 1/4000, 1/8000 = 6 stops
1 stop reduction = .3
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