I have done a lot of rebuilds on my
Rocket Mass Heater where I had to join old dried cob with fresh cob. The bond is never as good as the original however, there are ways to help make the joint as strong as possible. 1) Make sure your dried cob gets thoroughly wet.
Water it down several times and let it soak in. Just before applying the new cob, hit it again with a
spray bottle.
2) A thin layer of clay slip acts like a glue of sorts to help increase the stickiness right at the joint.
3) Make sure that the joint is not smooth or straight. A rough surface provides much more surface area and bonds best.
4) Try to make your joint in an area that may not be noticeable as much. Perhaps a seam where one colour meets another or flows with a design you've made so cracks won't be as noticeable.
I would think your insulation loss will be pretty much negligible.
Another suggestion would be to just remove a layer from the inside, apply the steps above and just re-plaster a new inside skin with a known good mix? Can you lay on your back and stick your head in there to work comfortable enough?