With much muscle & wall cutting the Kohler unit is in.
It seems to gush as advertised and desired. A few surprises tho.
We may need a larger hot water heater; especially if washing dishes or clothes simultaneously with bathing of a body.
There MAY be auxiliary heating going on.
Standing in the tub as it fills with warmed water, the fluid's temperature can be felt dropping. If the puddle is deep enough to cover jets that in-jetting can feel like it is topping up the whole bath heat?
Making the puddle deeper, quicker might happen were a ten gallon gas can (filled with water !) sunk in the pit where normally only feet go.
Pull it out after the bath water rises.
More to be determined by Archamedian experiment.