Most wipe on finishes are oil based and when they eventually evaporate, you will be left with the results you have seen.

The doors can be over sprayed with lacquer or polyurethane (oil or water based). Many of these products are available at big box stores in rattle can applications, in both gloss or satin finishes. If they aren't in stock, many mail order sources are available.

The problem is preparation, especially with the lacquer application. The original finish can have no contaminates, otherwise the new finish will end up with "fish eyes", which are small holes in the finish.

This is caused by any wipe on finish that may contain silicones or other product that will contaminate the new finish. The entire old surface should be lightly abraded with a fine grade of sandpaper or better  to use, various "grits" of Scotch Brite pads. The maroon or green colours work quite well for light abrasion and will conform to the routed edges of a raised panel door. Then the area should be degreased and dewaxed using a product like Prepsol or many of the products that are used in the painting preparation of automotive finishes.

Lacquer dries quickly and is durable for cabinets. Polyurethane is much more abrasion resistant, but takes longer to dry. If you can shoot the doors in your basement in a horizontal position, you will eliminate any runs or sagging of the finish. Use several light coats, sanding or abrading any dust before the final coat is applied.

This sounds complicated. It's not. Remove the doors and hardware, abrade the original finish, clean with a solvent and cotton rag, spray with the new finish. It's a definate DIY project. The result will be cabinets that will look as new as when they were originally built.

An addendum:

There are also wiping finishes that are available if you're not comfortable with spray cans. They are sold under many names and claims. You can make your own.

Purchase a quart of your favourite oil based varnish and some paint thinner. In a seperate container, pour in equal amounts of each and stir.

Using a recently washed cotton rag, (tee shirts and socks work well), wrap it around a small piece of cotton folded so that it is ball shaped, about the size of a large golf ball. Dip this into the oil mixture, making sure to saturate the inside cotton ball with the product. Scrape off the extra on the container's edge, so it doesn't drip. Apply the mixture to the wood, by dragging the ball shaped rag along the surface.

This will result in a smooth application of the polyurethane, and thinned, it will dry more rappidly. There should be no runs, and usually two coats can be applied in a day's time. Two or three are all that are needed. This also works well on refinishing furniture that is not an historical antique.

Again, the same preparation is needed to clean the original surface.

BOL