I have a 1995 Univega Via Carisma hybrid bike with 21 speeds.

How do I adjust the "Grip Shift" levers (left is a SRT300I-32; right is a SRT300I-71) and the front and rear derailleurs so the gears change correctly?

The levers work or they don't. It's really the cables and derailleurs that one adjusts. The levers only occasionally need lubrication. Here's a great source for learning how to work on your bike: Repair Help Articles | Park Tool

other than having checked the derailleur hanger for alignment at the bike shop.

cable adjuster at the Rear derailleur is all you got, with grip shifters..

In what position does each Grip Shift lever need to be in when adjusting the derailleurs

Front Derailleur Adjustment | Park Tool
Rear Derailleur Adjustment | Park Tool

Follow each procedure from the beginning, and complete each step before moving to the next, do not skip any.

My bike is in my garage; my computer is in my bedroom. It's about 200 feet between the two locations.
Since I have no other alternative, I guess I need to bring my bike into my bedroom so I can watch the videos while doing the adjustments.

Sounds like a plan. An alternative would be to watch the videos or read the information until you understand it, then go to the garage and apply what you have learned. Good luck!

After my retirement, my brain doesn't retain much (or really any) information for more than about 20 feet.

P.S.: The cartoon is from Tom Cuthbertson's "Anybody's Bike Book".

Sounds like someone needs to put an iPad at the top of his Christmas/Hanukah/etc. list!
See, that's how they get ya.

In all seriousness, there's no way you'll get it right after just watching the video the first time anyway, cause it's not a quick thing to do, so Take your time. End up watching the how-to multiple times anyway