Genius! But I never made it to the store.

Here is what I did:

I followed the procedure I outlined, and some suggestions gleaned elsewhere. I depressed the brake pedal, and held it with a length of 2x4. Then I removed the reservoir. The fluid level in the transfer ports did not drop, so I was not worried about air intrusion.

I did use non-chlorinated brake cleaner with the straw to clean as much of the reservoir as possible. I dried the the reservoir as best I could with compressed air. Then I used the methylated spirits (container said denatured alcohol) to clean again. Compressed air to dry, followed by two rinses with fresh brake fluid. I re-installed the reservoir, and refilled with fresh fluid.