a7RII+Meikon Case+ST-100 Strobe

That's right, 316 ms recycle time at minimum strobe power and 7 sec at full strobe power.

Yes, if the button could be kept depressed with tape, then a round rubber bumper attached to the mode selector rotator could work. Arrow 1 indicates a backup tab that would keep pressure on the bumper at the end of the rotator stem. Arrow 2 indicates the section of the rotator that could engage the mode dial. The small double arrow indicates the space between the rotator and camera housing which is larger than the space to the mode dial, so a bumper could engage the dial without interfering with the case. There is sufficient room.

I still have not gotten the strobe to fire on TTL. It should be straightforward according to the instructions and camera settings. On Manual, and 2 ft from the target, there is too much intensity even at the lowest output setting. I sent a message to Sea Frogs and expect a reply shortly. They've been very good about response time.

Thanks for information on the O-rings. The one in the case keeps popping out of the groove. Although it doesn't appear to get pinched if I leave it slightly out of the groove and close the case on it, I would rather have it lay flat to begin with. Meikon shows the same 155 mm for both the lid and case O-rings which is probably for convenience, but in reality the case O-ring should be slightly bigger.  Meikon's next stock size up is 165 mm which would be too big.