I looked into preserving eggplant awhile back. Canning is supposedly a no-no, as eggplant is dense enough that it is hard to get up to a proper temperature (without making the mushy mess you are trying to avoid). This comes from the government, and I know I can trust them.
Regarding preserving eggplant, have you ever lacto-fermented any vegetables? We've been doing so with cabbage, onions, radishes, broccoli, cauliflower, beets, etc. It's absolutely delicious. It's very simple too.
On some of the squash recipes and the pickle ones too, I've noticed it suggests putting in a couple grape leaves to prevent the vegetable getting mushy. I haven't yet tried squash OR pickles, but when I do, I will go ahead and put the grape leaves in.
Here's the initial recipe I followed for lacto-fermented sauerkraut. It's sooooooo beautiful (the deep pink/red color) and so crunchy. If you go ahead and give it a shot, use Himalayan Crystal Salt/unrefined sea salt (not table salt), and they also suggest using organically produced vegetables and filtered (not tap) water. We followed the recipe as shown, but then later found some glass weights to hold down the produce under the water level which we are now using. Either way, it works!
Preserving Food with the Lactic-Acid Fermentation Method: Sauerkraut Tutorial
Glass weights to use for fermenting
Another good link on fermenting