Sorry to hear you that your goals were not meet, yet.
Interesting read on j Type overdrive. This information was from a TR6. So it might be different.
J Type Overdrive Part I
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The pump runs all the time that the mainshaft is rotating. However, if the OD is sent for direct drive, the pressure relief is set to a very low pressure (~20 psi) and the pump has the very easy task of pumping oil to the mainshaft for lubrication.
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At normal driving engine speed of 3000 RPM, 3 X .033 or about 0.1 HP (about 75 watts) will be consumed. The OD might get a little warm but certainly will not get hot due to the pump energy. Note that this is not a precise calculation but probably has an error less than 25%, so it shows that the power consumed by the pump is negligible. There are other sources of power loss (heat) such as friction in all the bearings, bushings and thrust washers so the OD likely gets pretty warm if operated for an extended period.
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By his calculations in direct drive the loss should be minimal. How do the gear ratios without the OD compare to the old transmission.