So, I am currently looking into getting Ruby on Rails setup in a
shared hosting environment. I've looked into a number of the
solutions out there and the one that looks to suit my needs the best
is Passenger, but I know very little about Ruby on Rails overall.

I would really like this to be as simple as mod_php but many of the
Rails solutions out there seem needlessly complex, or at least too
complex to implement properly when our users don't have SSH access.
cPanel's implementation of using Mongrel, and running a separate
process for each application seems like a less than ideal solution.

I was wondering if anyone else had any experience or thoughts on this?
Is there any way to make Ruby on Rails work with as little
web-stack-side configuration as using PHP?

Congratulations for taking this first step.

Is there any way to make Ruby on Rails work with as little web-stack-side configuration as using PHP?

The short and unhelpful answer is no, or almost-no, and this goes for Python as well as any other language which would prefer not to be run mod_php like. The execution approach is different than PHP and likely to always remain that way.

Passenger is getting lots of attention. In Python land FCGI is one of the more popular deployment options although I suspect it will be WSGI (Apache mod_wsgi available) that ultimately becomes something of a defacto standard.

If you come up with an approach / billing model which works for your busines just for Ruby on Rails you should consider levering that effort by supporting any Ruby web app (other frameworks like Sinatra and such) and Python web app frameworks too (Django and others).

Passenger is fairly easy to get going with. It won't work without customizations with cPanel tho, because of the DocumentRoot that cPanel uses.

I saw this a while back but haven't looked into it much. Might be something along the lines of what you are looking for:

http://github.com/peppyheppy/cpanel-passenger

You could probably make it easier for your users by installing as many of the common gems as you can. Vendoring gems is sometimes iffy, and some gems won't vendor properly.