The maximum sync speed of an EOS-R is 1/200 any faster than that and the shutter curtain is not completely open during the flash pulse. It's characteristic of the camera and no escaping it except is you are using a HSS capable trigger and strobe. The only currently available strobe that is HSS capable is the Retra strobes (new series) . HSS works by pulsing the flash for the entire duration of the exposure, which is a long time compared to a normal flash duration. Consequently the max power of the flash is reduced. The G7X doesn't have this limitation as it has a leaf shutter that syncs at any speed.
Before you rush off and buy new strobes - do your homework to confirm the trigger and strobe combo you are considering support your camera model. The alternative of course is to reduce ISO and increase aperture and compensate by turning up strobe power so that your ambient exposure is where you want it to be - or for 100% flash lit macro shots the ambient exposure is much reduced and you are primarily flash lit.
If it were me I'd work on the basis that 1/200 is my maximum shutter speed and adjust my settings to suit. At 1/250 there will be probably be a narrow curtain on the image which might be acceptable. It should only be sunbursts that really struggle with the sync speed limitation - unless perhaps you are shooting fast action with large animals.
As for shooting Nemo, the usual approach is generally not higher shutter speeds, rather reducing ambient light by stopping , minimising ISO and compensating by increasing flash output.
As far as focus is concerned I would think it should be a bit snappier than with a DSLR -compared to a G7X, but you are working with reduced depth of field compared to the 1"sensor. What lens are you using? It sounds like you are dealing with the frustrating task of chasing nemo around his home - perhaps with a macro lens? Depth of field with the full frame sensor is less than the G7X, you need to stop the full frame down to f16 to get the same depth of field as the G7X has f5.6.
To help with AF, things like back button focus, combined with focus peaking to indicate when focus is right on Nemo can help with timing the shot.
