"Evidence appears to favor Flannery over a natural weak two-bid"
Not sure I would draw that conclusion. The difference in total IMP's doesn't strike me as statistically significant. Looks to me that the winning % strongly suggests a natural 2♦ over Flannery at matchpoints (a higher % of wins ...
"The question related to entering the contract into the BridgeMate, NOT writing it down in one's private scorecard.
"My practice is to ascertain the contract, write it down (or enter into BridgeMate), and then lead."
The emphasis in the OP seems more on the private scorecard than the Bridgemate.
By doing the same thing all the time there is no variance in tempo -- that's a good thing. IMHO, not much different than taking X seconds before leading, and arguably more consistent.
This may seem at odds with my earlier comments. I might put it this way -- it is ...