I think you'd be wasting your time to focus on anything but these people, ever.
Otherwise you'd be selling to the type of person that would find 10x the complexity from introducing a computer and the internet for every bit of simplification that your service provides.
My last landlord added me as a friend on Facebook when we signed the lease, and was actively attempting to use email and smart phones to facilitate communication. I've heard similar stories from other folks, so we may be at a tipping point where landlords are more open to SAAS tools, primarily because of the ubiquity of mobile apps and Facebook etc
What about modifying the initial workflow from the Tenants perspective and allow Tenants to make rent payments to Landloards who are not yet even on this site?
Seems like the easiest way to address your potential market (landlords) since there is certainly a huge demographic of renters who would like to use this service from the payment perspective. Changing the focus on the landing page to be directed at the Tenant -- as in PAY YOUR RENT NOW, and focusing on the benefits to the tenant as part of your conversion process.
While I would love it if you'd prove me wrong (go, do it! be a success!), your responses here appear a little naive. Spending 2 years building something like this is very impressive, but it doesn't sound like you've talked to very many customers. (I get that just from the vague statements you're making about "these days", "starting to realize", etc.)
I know nothing of the space, so I can't comment to that. But it does sound like you would benefit greatly from doing some customer development, Steve blank style.
Like I said, I know nothing of the space, so I wasn't even aware of competitors. I think that's good news that there are others already succeeding, now you just have to do things better than they do!
That said, how do you know they're doing so well?
Another spin on the idea that I'm sure you've thought of: what about targeting this software to a bigger client, the companies that run apartment buildings? Include a notification system (so they can notify all building residents), and you could start to build building-based online communities. Anything like that in the works?