But it's all worked out.

When they told me they couldn't replicate the problem, I told them "just change the transmission fluid". Service Guy kept telling me that he thought it was an adjustment problem, not a fluid problem, but I insisted until he agreed to have it done.

And lo! the car shifts much more readily into Park now. I think that it will be fine after a few more days of driving and/or when it warms up a bit.