Where should I submit my upcoming game?

I’m finishing up a game now that should be ready for release in a couple of months. It’s probably not going to be complete in time for the Spring Thing competition at the beginning of April, and it contains some already-released content that makes it ineligible for IFComp. Is there another competition in which I could enter it? Rather than winning a competition, my goal is just to find people to play something I’ve spent quite a lot of time on; if I were to just put it on my website, for example, I don’t think anyone in the small IF community would notice. (Also, I don’t have a website.) Is there another competition besides those two that gets a decent amount of traffic, or is there another way to find an audience for the game I’m writing?

If your game has a horror theme, you could enter it in the Grand Guignol category of Ectocomp near Halloween.
There is also usually a New Year’s comp. Both are very loose and not for prizes, but people will check the games out.

Alternately, you could plan and promote a game jam that your game fits into, and encourage other authors to write or enter some similar games to release along with it. Make sure the category is broad enough that other writers will be interested and be able to work within it and that there is sufficient time for others to write games… itch.io has tools to plan and run a game jam, but you could always do it yourself. Promote on Twitter, Facebook, and other social media.

Dropping a game blind on IFDB can be frustrating. You could always point people to it on social media, and very politely privately request some regular IFDB reviewers to write about your game on IFDB or a separate blog, especially if they have a blog syndicated on PlanetIF. (Of course, don’t do this unless you end up deciding not to enter a Comp.)