Alright. In a way, we gave up on our logging out during checkout problem. When we finally managed to narrow down when it was happening, it pointed towards an old version of the STRIPE HikshopPayment plugin, so, rather than bang our heads against that wall, we upgraded to the current one in the Hikashop Market. There's still an issue, but we're not being logged out.
The issue was so bizarre, I will summarize it for you, but I have no more questions about that other than idle curiosity. Basically, a registered user would occasionally be forcibly logged out of Joomla during checkout. What we finally managed to find was a repeatable pattern to trigger it, yet it still makes no sense.
I put logging code into every OrderAPI method (inserted into our plugin) and PaymentAPI method (inserted into the old Stripe plugin) which would just record the trigger name and the User's ID at the beginning and end of each trigger method. What we learned was that the User remained logged in before the order creation, through the payment plugin initialization, but was forgotten before the payment plugin received notification, and remained logged out through to the thank you page. HERE'S THE REALLY WEIRD PART. The site worked in all browsers but Chrome, but it didn't always fail there. If we quit and restarted Chrome, logged in as our user and placed an order, it would log us out. If we logged in again, it would succeed from that point on for multiple orders, even if we logged out and in again. Even if we emptied the browser cache. But always on the first time through, after a fresh restart, Chrome would forget its logged in user during checkout 100% of the time, on PC and MAC, -- always right before the payment plugin handled a transaction notice, yet the order was being successfully confirmed. Since it always happened when the payment plugin was busy, we blame it - but I don't think I could program that behavior if I tried. So we updated the payment plugin.
That issue seems to be gone, but the payment plugin's still temperamental on my partner's Chrome browser for Windows 10 - it won't allow any credit card to be submitted, (valid or test value) and when it fails - there is no message, nothing in the debug log, and the cart gets deleted. (we even shut off ALL Chrome extensions). He's going to test from a different PC tonight.
Like I said, I have no questions right now, I'm just completely baffled by ALL of the weird errors we couldn't figure out. I'm switching back to problems I know I can solve for the night.