It can't hurt to check the regulator/rectifier, but I have jump started my old XJ600S (electronic regulator/rectifier) and my CB550 (mechanical regulator/rectifier) several times over the years with no ill effects. I have heard of people who have accidentally reversed the wire polarity when jumpstarting and blown electrical components, but I have never seen that happen from normal jumpstarting with booster cables done correctly.
I absolutely would AVOID jumpstarting if at all possible, however. The best bet is to get yourself a good automotive battery charger that shuts off automatically (you'll need it for the rest of your life, anyway), set it at 2amps or less to charge, and charge up your battery fully.
In any event, the regulator/rectifier is not the cause of your running problems.
So, you know that you are getting spark, right? You also know that you have good compression because you ran the compression test. So what's left?
You also need fuel and air.
Check your air filter (yes, pull the tank, I'm afraid. It really isn't that hard). Maybe a mouse or a squirrel made a nest in there or something.
Check your fuel delivery. Are the spark plugs wet when you pull them out after trying to start the engine unsuccessfully (with choke on, of course)? Are all four of them wet? Does the engine fire at all?
Could your petcock be clogged? Could your carb jets be clogged? You must put the petcock on the "Prime" position, since those bikes have a vacuum actuated petcock for safety reasons in the event of a tip-over.
Could the vacuum diaphragm in the petcock be cracked or leaky? Connect a hose to it and see if it flows fuel when in Prime. Try again while you apply vacuum to the vacuum line (a MityVac would be a great tool to own for this, too). If you apply vacuum to the vacuum line (careful not to drink any fuel here - use a Mity-Vac if you can), does it hold the vacuum?
Could the fuel pump be defective? Your bike has a vacuum driven fuel pump, too. Apply vacuum to it and see what kind of flow you get. This is a common failure mode, I understand. I've seen that other owners have upgraded their fuel pumps to the electric fuel pumps available on later years (in Europe, at least).
So, first charge up that battery properly, and then get back into the game. Don't give up. I really love those bikes, and still regret the day I sold mine.
I would check the regulator/rectifier on the bike. From all the charging and jumpstarting your doing I would say that it's toast, or at least getting there.
Get a multimeter and test the RR, and all relays
Some nice diagnostic instructions here
http://www.electrosport.com/technical-resources/diagnosis-center.php
BTW every time i've tried jump starting from anything I have had to replace the regulator/rectifier. The batteries are 8 amp on these bikes, if the electrical system gets hit with large amperage it seems to fry the RR. I could be wrong, this is just from personal experience.