Rest assured I am very familiar with the safety concerns of a pressure vessel. I deal with them daily.
Like the others, it is hard to get past the irony of "being quite capable" and yet not knowing what to get or where to get it. I think that most people would have the same concern, for both you and your wife, who is the one who discovered the leak.
The professionals I've recently had a chance to meet who work with pressure vessels every day have ultrasonic thickness testers, and follow a regular schedule of checking tanks for thickness, and therefore would likely have proactively discovered the tanks condition before their family members did, either innocently or catastrophically.
I sure wish I had access to a UT tester. If I dealt with pressure vessels daily at work, I'd certainly avail myself to whatever tools that OSHA requires in the work place for periodic tank inspections.
I'd also know to look at the welded tag on the tank and note the National Board registration number. I'd contact the National Board and order the MDR for that specific tank. The NB has records of all ASME certified pressure vessels made since 1929. I'd order the U1A report for the tank. You no doubt know what all these acronyms mean, and how to order the report, etc.
And you also no doubt know that the report isn't entirely necessary, because the most basic information is already stamped into the tag on the tank, including the minimum shell and head thickness at the MAWP. It may even have the material type used. If it doesn't, then the report might be helpful if ordering a new head for the bottom.
Also, you probably know that the steel used in pressure vessels has particular characteristics... there is a very large spread between the yield and tensile strengths, typically 45ksi y to 75ksi t, and there are other properties that justify why just regular ol carbon sheet steel is not as suitable as the steel that is optimized for air receivers.
So, assuming that you already know that the SA414 Grade G is the most likely and probably the most suitable material used for that type of tank, then maybe you were just wondering about the ratio of the head as an engineered element of the end bell of a tank. Even without your experience, you might have noticed the stampings on the ASME tag welded on your tank stated 2:1 Elliptical ratio.
A quick google of these terms... tank head, SA414G, and 2:1 Elliptical Ratio reveals a smorgasboard of useable links on the first page. Even the first line hits on sources of pre formed tank heads. You might have some of these companies on the rolodex at work, but in case that rolodex is buried under all the other pressure vessel testing welding and procedures piled on the desk, here is a link to get started...
http://hansontank.us/semi-elliptical-tankheads-12-20inches.html
Some already have a beveled edge. Some have a square edge. It depends on how you want to join the seam... **** weld or lap weld, with lap being the most typical for the girth seam holding the head. The U1A will state how the OEM did it, and what percentage of efficiency you might be trying to match with that seam.
Of course, the heads don't come pre drilled, and don't have a thicker bung welded on for material to tap NPT for a drain hole. But that's probably just an inconvenient nit for someone with your experience. No big deal.
Minimum order is $400... which of course would by a new 60 gallon tank or even an entirely new or nearly new Sears 60 gallon compressor.
You'll have to weigh the cost benefit ratio of welding onto an already thinning consumer grade tank from Sears that has been exposed to 20 years of fatigue stress and thermal cycling and may not have been maintain, much less periodically inspected/tested, for much of that period of time.
Your experience and professional exposure to pressure vessels will no doubt guide you to the best course of action to take, without anyone's help on an internet chat board of home garage enthusiasts.
