I thought that I would jump into this discusiion as I have some relevant experience. My background is in physics and optics (24 years). I have designed optics, managed the design and manufacture of optics by contractors (including 2 space instrument designs by Leitz).
To recoat the lens, the existing coating will first have to be removed. This will be done by polishing with an abrasive compound. The radius of curvature of the front end of the front element may change and the thickness of the front element will be slightly reduced. These changes may affect the image quality. Without the lens prescription, it is difficult to predict the affect on the overall lens performance.
The lens can then be coated, but the coating must be designed for the specific spectral range and angles of incidence. The spectral range is easy to figure out and the angles of incidence can be reasonably estimated with some judicious ray tracing with an optical design program. The coating will not be the proprietary T* coating, but it can be an excellent coating. The coating may have to be designed by the coater, if they don't have one in their design "catalog".
Given that you have to dissassemble the lens, polish off the coating, recoat the lens and reassemble/align the lens, I am estimating that the work will cost you about $3,000 to $5,0000. There are places that can do this work, but they may not be interested, as it is a small job for them and they don't always like dealing with "amateurs". If you find a place that will do all of the work for less than a few $k, then you should be very cautious.
If the scratch is really bothering you, buy another lens and sell this one on ebay. The 80-200's are going for ~$400 on ebay, with a maximum of ~$750. They seem to show up regularly. You won't get the maximum price for yours, because of the scratch, but if the price differential is $400 between what you sell yours for and what you pay for another one, you will have only spent 10% of what it would cost to repair the lens and had much less aggravation and probably have a better result.
There are good reasons why replacing the front lens was quoted as an astronomical price. It has to do with hand building one item versus mass production. Replacing one lens is a hand-built effort.
My recommendation is to buy another lens, rather than try to get the lens recoated.
Good luck, if you decide to recoat. I wouldn't. I would rather put the $4,000 into a few more lenses.
Regards,