How can I use up massive amounts of wine vinegar?

susan, couldn't you write to the editors and see if they might want you to do a feature?

Make infused vinegar to give as gifts.

You can use the red wine vinegar for marinating beef for Sauerbraten. I put white or cider vinegar in a spray bottle and use it around faucets to dissolve the lime and other minerals that build up.

wow, susan, i knew you were something, but REAlly, your own cleaning supplies? you are one hot ticket!

Lots of good ideas so far.
There are also several uses in house cleaning (e.g., mix with baking soda for a non-corrosive drain cleaner) and personal care (e.g. as a rinse after shampooing), especially for white and cider vinegars. Web search will turn up many ideas. As always, be sceptical and careful...example, some advise using it in machine washing clothes, others say it corrodes soft (rubber or synthetic) fittings of the machine.

Doesn't red wine vinegar have a short shelf life once opened? Approx 6 months?

Red wine vinegar: pickle red or yellow beets in it. Recipe in Virant's "Preservation Kitchen." If you pickle golden beets in it, add a red beet to make them a gorgeous sunset orange color (what I call "luminous beets" in a recipe with the same name here).
Save several gallons for the summer time and use it for pickling other things. Any recipe that calls for "white vinegar" (bleahhhh. I agree with Kevin West that white vinegar should be kept in the cupboard with household cleaning supplies and used for no other purpose) and in many cases, cider vinegar, will be better when made with wine vinegar. Confirm the acidity level on the label (must be at least 4.6 for safe pickling or other canning), remembering that a lower number => greater acidity. Good discussion with accurate details on this topic here: https://food52.com/hotline/16762-pickled-shallots ;o)

You could use some of it to make a shrub cocktail. Lots of shrub recipes on Food52

You could quick-pickle some vegetables in the red wine vinegar.

Catsups and chutneys can use up a lot and keep well, but you're probably fighting a losing battle. Some people use boiling vinegar to clean off burnt on foods, but it reeks horribly and baking soda works better anyway- you certainly wouldn't want balsamic for that.

I agree with CV. If they are sealed, donate to a food bank. They must be sealed though because they operate on the same rules and guidelines as grocery stores. If they aren't sealed, you could portion them out and gift to friends.

Something fun to make with balsamic is a balsamic glaze. I don't know where the recipe that I used came from, but it's brown sugar and balsamic reduced on the stove until it thickens to a glaze to your liking. Delicious on meats.

You can use a cup of red wine vinegar with braised chicken. David Lebovitz & NYT has recipes for this dish.

I would donate to the local food bank, not worry about trying to deal with it. This is more of a storage headache than a cooking challenge.