Pull the outer power tubes from the twin for half volume, buy a JBL E120, and get the SG modded with a Super 2, OR Dual Sound in the middle. Jerry used Dual Sounds in Tiger untill 82. That should get you pretty much there!
I had pretty good success with that early 78 tone by scoring an 81 carvin dc160 and going with a dual sound in the neck, and using a 10db boost through a twin. If you have a middle pick up you can blend with the neck and get really great tones as well. I have a PRS CU 22 with a dragon 2 at the neck and a dual sound in the middle position. With the neck on single coil and the middle on humbucker mode it's even more tiger like.
The carvin mimics the wolf as its hard rock maple and a hard tail. That early 78 jerry tone has some gain to it and I suspect that's the stratoblaster working with the dual sound. If you listen to say dicks picks 18 - Those Wisconsin shows and listen to the eyes you can here jerry up at the 18th fret high e and it sounds like a lower note because the dual sound handles those high frequencies different than the supper 2's. I think that is the essence of the 78 tone.
I came across an 82 carvin on our local Craigslist for 450 just last week. I think chasing the 78 tone with a mahogany plank and rosewood fretboard will be a challenge. I would be warry of starting with the wrong guitar. Spend your money wisely so find a better axe than the sg. Just sell your sg and look for a carvin or prs se if you are on a budget and build around that. Next look for a used blues deluxe, fender deluxe reverb or a cheap twin,which these days they are giving away. Then score a jbl speaker. If you go the deluxe root you only need to fork out for one speaker.
Interestingly the shorter neck scales of my carvin and prs do seem to effect the tone that much when I compare them against my strats and I just scored an 82 strat that sounds as good as my prs and just as Jerry like at a fraction of the price. Again, the dual sound for me is the way to go. I've got it in both my prs and carvin and I'm with you on the chase for the 78 tone. It's my fav.
The speakers - jbl and the pickups are the first places to start and a dual sound in the neck gets you almost there.