Hi Tricarb,
Well, so the cancer is deeper than originally thought? At least yours is running and the engine compartment looks great. I have a few suggestions too, which may help:
1) there is a video sold by the Healey Center in the UK that will give you insight on what a full restoration of one of these looks like, done by specialists in the field. It is quite informative and well done. I paid 20 bucks for a copy on ebay some time ago, but unfortunately loaned it out and haven't seen it since (or I'd offer it on loan).
2) I bought and still use the MIG sold by Harbor Freight specifically to do my healey. It is a very basic unit, made in italy, with low output. It will only do sheet metal, will overheat if you try to weld too long of a bead, and the heat only has 4 settings. I normally keep it on high only. That being said, it has been reliable, is still working now, 10 or so years later, and I do use it often as it is easier to set up than the TIG, gives a better looking weld than the arc welder, and doesn't spread the heat like a gas welder (I do have all these too - aquired along the way with the Healey rebuild). If I were to do it again, I would get the small MIG by Miller. They have great support, are sold and serviced locally, and are a quality machine. The TIG I own is a Miller (the small, hobby version) and I'm very happy with it.
3) If you choose to take on this work, it will be a long journey but you will learn alot along the way. If I were to do it again, with a car in your condition I would seriously consider taking it to a shop for the metal work, if you can find someone with the skills and experience needed. I had my front frame member replaced along with other bits by a specialist in southern cal, and was never sorry for it. He aligned the frame, did the replacements, and all with excellent results. Unfortunately I ran out of cash and had to take the car back before he did the fenders, sills and rockers. So I had to replace those bits. What a chore!! And figure you'll have to do things twice at times as you are learning. Everyone I talked to recommended the Kilmartin panels for replacement, and they worked out well. They are slightly thicker metal than original, but the curves fit well with minimum 'sculpting' to weld them in. Sheet metal is a bear to weld since it warps so easily, and there are long flat sections in the front fenders where the rust repair panels fit. The video by UK Healey Center shows them soldering on the rust panels after flanging them. This is probably a much easier way to do it than the welding. You end up with a straighter panel in the end, but perhaps not as well rec'd by the purists.
Be aware too that this isn't a car like others. All panels were semi-custom fit at the factory and even new panels need fitting. If you do take it to a specialist, he may do the repairs without removing the fenders as fitting the repair panels often requires the other panels in place to ensure a good fit. Once tacked in place the panel can then be removed for final welding and body work. Keep the engine and drivetrain in the car during these fittings so the frame will be flexed into the proper position. The doors can flex up about 3/8 inch in some cases between having the engine/etc. in place vs. not.
4) It will cost 2 to 3 times what you originally estimate. That is a given, even if doing it all yourself. If you take it to a specialist for the metal work, you can still do the time intensive body filler, paint prep, etc. and then send if off to a painter. That could save you alot of $$. I am about to send mine off for final paint, and was quoted $2500 for finishing it with a Dupont paint system. Don't use POR if you can avoid it. Get the rust either blasted or totally removed. And if blasting, use a very fine mineral type blasting, and coating with epoxy primer. The fine mineral material is small enough to get into the pin holes created by the rust, doesn't warp sheetmetal, and the epoxy primer adheres excellently to the metal so the paint won't chip. Use a paint 'system' too, sticking with the same vendor's products so it all will work together....
Well, good luck with your project. I'm envious of you having a car in such good condition from which to start. Just don't get discouraged. In doing this and other projects I've found that if you do something on it, every day, no matter how trivial, will keep it going and in your mind and progress will occur.
Jerry Rude
10 years into a 3 year restoration
Hi Guest!
Hey - did you know if you click on the title of a thread it will take you to the first unread post since you last visited that thread?
but were afraid to ask: 
STOP!! Never post your email address in open forums. Bots can "harvest" your email! If you must share your email use a Private Message or use the 
smilie in place of the real @
Pretty Please - add it to our Events forum(s) and add to the calendar! >> 
)