From my most recent test drive, I believe I have found the solution. The issue appears to have been a combination of a bad petcock as well as a partially clogged vent. Instead of trying to clear the vent and risk getting crud into my gastank, I got the vented gascap from an 80's Honda Magna, and the issue is completely gone. I'm sorry it took so long for a post update, but shipping took forever and one of the parts was no good when I got it.
The first gascap I got was used, and all of the rubber had hardened into glass. It shattered when I tried to flex it, and all of the guts were complately frozen with rust. A soak overnight in vinegar freed up the mechanism, so the key operated normally, but the little mylar(?) membrane in the vent went brittle and allowed air in and out instead of just in. This, combined with the fact that a replacement rubber seal is not separately purchasable led me to demand a refund from the eBay parts seller.
It took some time and way too much money, but I finally got a new in box part from eBay. $100 for a gas cap was tough to swallow, but if it would work then it would be worth it.
The part I got was in a box labeled with part number 17620-MB1-033. There are several part numbers you can find for this gascap, but I can see no rhyme or reason as to which ones are vented and which aren't. I know that the first two revisions of this part do include the vent, but later revisions are unvented like our Valks. Pictured here in my hand is the original Valk part, and installed is the vented Magna gas cap. If you're looking for a vented cap, the cap must have that black-capped protrusion, as that houses the 1-way vent, which is friction fitted in that tube by an o-ring.
In any case, after swapping the gas cap and filling up on fresh gas, I went for a test ride. I was no longer able to reproduce the issue. Hopefully it stays that way, even though I've only gone for one test ride of about 30 miles. If it doesn't, I'll be sure to post here again.
Thanks again for everyone's help! I really appreciate your support and assistance.
Happy riding!
EDIT TO ADD: A 75 mile ride today confirms the issue is resolved.
