First, DO NOT FLUSH the transmission or DO NOT HAVE IT FLUSHED. Yes, this advice does go against what you may have heard or read elsewhere, but, there’s a huge problem with flushing, especially in an older transmission. It has to do with the way the flush works. To flush a transmission, a hose is attached to the transmission fluid filler assembly and is pressurized quickly, blowing everything out of the transmission, fluid, deposits, bits and pieces of metal and anything else that may have accumulated. In turn, the pressurized material surges through every part of the transmission scourging the passages, channels and galleries clean. However, in that comprehensive pressurized cleaning is also the problem — larger objects can damage delicate transmission parts and may either create problems or enhance existing problems. You see, the pressurized shards that may be blasting around the bell housing can also take pieces out of parts of the valve body, knock out tiny, but important, check valves, damage rings or clutch packs or more. So, instead of using a flush, simply drain the transmission through the drain outlet, allowing as much of the transmission fluid as possible to drain out. Admittedly, this will leave about a quart inside so what you will have to ask your transmission shop to do is drop the pan to remove the last quart and, if they find nothing on inspecting the pan (they will likely find grit and gunk in the pan and, possible metal shards if there is metal-to-metal contact) asking them to reseal the unit. After it is resealed, add new automatic transmission fluid to the proper point and you are all set.
As to your specific question, since the Galant has 193,000 miles on the clock, it is only appropriate to remove the transmission fluid and replace the filter. The color of the transmission fluid tells you that, since it is brownish-black. It also tells you something that you should find very hopeful — there may just be nothing wrong at all with the transmission.
If the transmission fluid was totally black and somewhat thick it may indicate that the fluid has started to burn. Burning indicates that heat is being generated somewhere, usually from metal-to-metal contact such as bands or gears rubbing against one another and wearing. Since the transmission fluid is organic it can burn and if there is heat being generated it then will burn and pick up a burned odor. Pull out the dipstick, when you have a moment, and take a sniff of the fluid, if it smells burned then you have an overheat problem somewhere that is likely caused by metal-to-metal wear. However, since you did not indicate that there was a burned smell, it likely means the only item of wear you are describing is the color of the transmission fluid.
With 193,000 miles on the Galant, it is quite apparent that the transmission fluid should be worn and its color should be changing to black-brown. Since there is a brownish tint to the fluid, it really does indicate that it is just old and that there are unlikely to be other problems with the fluid, itself.
Yes, it is a great idea to drain — properly — the transmission and replace the filter and then refill with the proper transmission fluid. However, here is where the issues may start (you indicated you were worried about this in your question). It is very likely that over the length of time the fluid has been in the transmission things may have worn down and dirt may have built up in some places. In other places, it is likely that deposits may have settled out of the fluid and onto transmission parts. The reason the deposits form is because the transmission fluid has lost its detergent characteristics, allowing the deposits to start up. It really doesn’t matter whether the deposits are on the blades of a clutch pack or are located in galleries within the valve body. What matters is that the deposits exist and what happens when you introduce new transmission fluid.
Because the detergent characteristics have been restored, the deposits that have existed are likely being cleaned, exposing surfaces that have not been immersed in transmission fluid in a long time. It is possible that the deposits may have leached out some of the metal or that metal filings may be trapped in the gunk that makes up a deposit and when the deposits disappear the shards are then free to go throughout the transmission potentially damaging other areas. Further, since fluid flows may have been reduced by the deposits, restoring them to full pressure could easily damage old parts, causing them to break and causing further damage.
All told the time has come, the transmission is saying, to think of replacing it. It certainly doesn’t owe you anything — neither does the fluid but that’s another story as was just noted — and, if you get another 150,000 miles out of the Galant for just the investment of $2,800 for a replacement transmission, then you are still coming out ahead.