Not too late to switch to smaller at all - I have the six quart Sterilite shoebox tubs (three of them) as well.

There's no way for the probe to be knocked off the side (no gap between the egg box and the side).

And yes - very likely all three clutches will be in at the same time, although the third will be about 30 - 45 days after the second clutch (she just ovulated earlier this past week).