There is indeed a combination of things I think could help, but it may take a little bit of elbow grease on your part. Two years is a long time for a red wine to live in a carboy and I’m not surprised that you’ve had some deposits on the inside of the glass. Those deposits likely consist of an agglomeration of tartrate crystals, condensed tannin structures, and possibly some tiny lees particles and other gunk. Understandably, you don’t want all of it to be on your carboy the next time you make a batch!
The first thing I would do would be to soak those carboys in warm water and then add a couple of handfuls of something to be used as an agitator like BBs, buckshot, marbles, or even fine gravel. Let it sit until the water has cooled down to just “warm.” Now here comes the elbow grease part: Dump out enough of the water so you can pick up the carboy and give it big sloshes back and forth. The goal is to use the agitator to loosen up some of that crud on the sides of your carboy. Keep rinsing out the water (keeping the agitator inside) until you can’t get any more of the deposit out using this method. This is essentially your “cleaning” step. Then I would soak the carboy in a warm-to-hot solution of sodium percarbonate (sometimes sold as “ProxyCarb” in home winemaking stores) overnight. I would use about a half cup for a 5-gallon (19-L) carboy. The next day (wearing gloves and safety goggles), I’d pour out some of that solution, toss in my agitator again, and give it some more sloshes back and forth to loosen more sediment. The idea is that the chemicals will have time to work on the remaining crust overnight and the next day you’ll be able to manually loosen some more.
After applying this high-pH solution to dissolve some of the matter, if you’ve got more work to do, I’d follow this with a citric acid rinse (about 2 Tbsp. in a 5-gallon/19-L carboy) and soak it overnight in a solution of about 5 Tbsp. citric acid to a 5-gallon (19-L) carboy of water. Sometimes this will help dissolve other particles that might have been resistant to the higher-pH solution. Do a final rinse with water once you feel you can’t do any more. If there is a little bit of sediment left sticking to the sides of your carboy I wouldn’t sweat it too much. These carboys should be fine for fermentation and even for long-term wine storage if you clean and then sanitize them well ahead of time with something like a quaternary ammonia compound (sometimes referred to as “quats”) solutions, which can be purchased from most home winemaking and brewing supply companies.
Just as an aside, have you tried one of those angled-neck carboy brushes? Most home winemaking supply stores sell various types that are specially designed to reach into those awkward angles and corners. I’m guessing you’ve not been able to find one that is a good match for your carboy . . . and at any rate, sometimes carboy brushes just can’t exert enough pressure on stubborn deposits. Though, if you can find one, in addition to the solutions mentioned earlier, they can be quite helpful.
