I'm worried that something has changed in the 30 years and maybe people are doing things differently now than they were back then
You mean people jerry rig some ill engineered, rube goldberg, additions to their machines because they don't believe Honda knew what they were doing 30 years ago? Is this the "something-has-changed" to which you refer?
If you could go back to 1975 and drive a CB550K off the show room floor through a time portal to 2007, it would still be the reliable machine it always was and work the same way.
Okay, I just read your demon-possessed-transmission paragraph. The shift lever has a spring return to move the lever back to a central position. In first gear position, you can push the lever against the spring and it won't do a thing but spring back. Lifting up will get you neutral or second depending on how far you make the lever travel. Shifter operation is explained in the owners manual.
Some of your jumping-out-of-gear behavior could be attributed to a chain with tight spots. (have you replaced the bad chain and sprockets yet?) Have you tensioned the chain while is it positioned at the tight spot?)
A dragging clutch (one that does not disengage completely) can create all sorts of transmission issues, some of them permanent. So, if you wish for your machine to survive, get them sorted quickly.
The first thing to do is verify that the clutch is adjusted properly. The shop manual explains how to do this properly, even if the information is 30 years old.
Next thing to address is the engine oil level, oil type, viscosity, and oil age, as the clutch is bathed in engine oil, that can effect its operation. This is where your concerns that things have changed in 30 years become warranted. As oil formulations HAVE changed in 30 years, automotive oil in particular. 10-40 W is still valid. But, avoid energy conserving labels oils intended for modern automotive use. For simplicity sake, use an oil that has motorcycle use labeling in it. I've read claims on this forum where 20-50W oil helps dragging clutches. I merely relay this information. I can't confirm it. I use 10W-40 in all my Hondas year round.
It may be that adjustments and correct oil conditioning won't fix your shifting issues. This may then require replacement of warped clutch discs inside the right cover that won't stay flat as the temperature rises, causing clutch drag.
The machine operator can compensate for a mildly dragging clutch without risk to machine or personal anatomy. The transmission shifts more easily when the wheels are in motion. Toward that end, make all your gear selections while moving and anticipate when you will need a gear change and make it in advance. Find first gear before you stop. If you are stopped, neutral can be found more easily if you rock the bike fore and aft some as you apply gentle pressure to the gear lever. If the bike is jumping forward when you select ANY gear. Fix the clutch NOW!
A dragging clutch or one that won't disengage properly can lead to damaged transmission components, shift forks, shift drum, and gear dogs are among them. These all require engine removal and lower case separation to address and correct.
From the issues you are relaying about your bike, it would appear that it has had an unfortunate maintenance history with some pretty ignorant motorcycle handlers who avoided professional help. I'd advise you to play "catch-up" quickly, if there is any hope the machine can be made fun and reliable again.
Cheers,