This thread is turning out to be very long considering it is about a simple SG-8 sig gen!
Heathkit products had to make some compromises because they were kits that could be assembled with simple hand tools by someone that did not have a lot of electronics knowledge, they had to make the products cheaper than factory made products. They were a great way for folks to learn about how electronics were made. Not everyone were successful with assembly however.
After looking at the thread on the other forum and the Radio City Products generator, I have to commend you on your goals given your problems.
So a few things. When dealing with RF you need to keep in mind the whole reason it is used to transmit signals, it can travel through the air (space). Every piece of wire is one plate of a capacitor, any other piece of metal nearby is the other plate, so the signal can travel for one to the other. To a lesser extent every wire is also an inductor. It comes down to "lead dress", how wires are routed from one place to another. Wire carrying RF need to be as short as possible and not pass near other wires or parts that could effect it or be effected by it. I think the wire you added should have been kept away from the parts that are in the oscillator circuit. It would be better to go from the output pot terminal, through the cap and the then the BNC connector. Keep it all near the front panel, that way if it couples to anything it will be the grounded case. In fact using a piece of coax cable (with a grounded shield) would be better that a single wire. Wire dress is not shown on schematics and is something that has to be learned.
Another thing, never assume that something that is not touching when you close the case will stay that way. A year from now you could bump the generator on the bench and your connection to that cap could move and short. Fasten parts in place, don't depend on thinking things will not move unless they can't.
Troubleshooting an RF oscillator circuit is difficult and much more so without more test equipment.
On the bright side the Radio City Products generator looks to be a better design. That will have to be a separate thread of course.
I'm sorry I don't have the time and resources to be your tutor. You might want to find an old copy (say 35th to 55th edition) of the ARRL Radio Handbook. ARRL (American Radio Relay League) has published their handbooks since the 1920's. The first several chapters contain info on electrical laws and circuits as well as design technique. There is also a website.
http://www.arrl.org/tech-portal