My advice would be to write more detailed requirements/specs, along with a feature list (including the front-end, the interface, the online service integrations, etc.), and hire a couple of experienced programmers in parallel to do a proper technical analysis and quote so that you can compare options and make sure the numbers you are getting are in the same ballpark and reflect a similar understanding of the complexity of the project.

How would you go about hiring programmers to do that, and how much would it cost?

The thing I don't understand in your original post is that you're not mentioning gameplay. Will your game only contain menus? It's good to know the UI and social functions you want, but it's probably not the core of your game?

It is, actually.  It's a very simple typing game.  I would provide more information to a programmer than I have in this thread, but honestly not much more.  The most difficult part, I think, would be the Leaderboard and Steam Achievements.  Then things like Steam trading cards.  I want to "check all the boxes" I can on Steam.

It's really more an art/novelty project than a game.  It's almost an incremental game only your task is typing instead of clicking.

Do you think a profit split would work better?

I've only commissioned art on work-for-hire basis.  Artists don't seem to be willing to do a profit split.  So I thought I'd approach this as work-for-hire.

A partner would be great, but that would be a whole other arrangement.  I wouldn't pay up front, but would split profits.

So, as an alternative to my original question, how would I find a programmer partner?

I'm still mainly interesting in my work-for-hire approach.

I'm thinking about commissioning a programmer for a game I want to make.  It would be on a work-for-hire basis, a one time job.

It's a fairly basic typing game.  There would be a Title screen (I'd give him placeholder art to work with), a HUD that tracks various stats, and a Hall of Fame screen that records final stats.  There'd be a settings menu to adjust window size/fullscreen and volume options.

There would also be an online Leaderboard and Steam Achievements.

I'd want everything well-organized and commented so I could swap out art, text, and music myself.

How would you recommend going about hiring someone for this?

How much do you think it would cost?