Do you want your art to be picked?
I know, I know, you’d like both. Who doesn’t? Institutional validation is a powerful thing. And let’s face it, it’s far easier (and cheaper) if someone else does the heavy lifting of producing.
The first question to ask…How important to you is this particular piece of art that you created? Is it disposable? Meaning, you finished this one and it’s on to the next. Which is perfectly acceptable.
Or…Is this one so important, so personal, so meaningful, that even if it’s not chosen by an institution for production, you’d still produce it yourself?
If yes, why not pursue two paths at the same time and set a deadline. Submit to those institutions you admire and respect and think would do a kickass job with your art. But if by the deadline date your art is not chosen, be ready to step up and produce it yourself. (And when you do, make sure you send a thoughtful invite to those institutions you first sent your art to. Play the long game.)