I installed Genymotion. Getting it configured with Themer took some doing, but once it was setup I had everything I needed. Thanks so much for this suggestion.
For those who want to do the same thing, there are some things you need to know. First, you need either a Google account or a Facebook account to log into Themer. That means that after you install GenyMotion, you need to do one of two things: either you need to 1) flash a Google apps package over the GenyMotion VM (a 4.3 apps package that works with Cyanogen mod works best), then log into Google, then update everything with the Play Store, and then install Themer; OR (and I didn't do this, so it might be more complex than this) sideload Facebook and sideload Themer, log into Facebook, then setup Themer.
The reason you need to do this is because in order to use Themer, you need to log in using either a Google account or a Facebook account, and Themer uses a list of accounts already on your phone (or in this case, the VM) to populate the dialog box that asks you to log in. That said, you want to have either a Facebook account or a Google account set up on the device (or VM) prior to launching Themer. Since I'd rather not ever use Facebook to do anything, that limits my option to Google.
It might be the case that if you exported themes from Themer and wanted to import it, that you might not have to go through any of these steps. However, if you want to be able to download existing themes from Themer and work with them as a starting point for building your theme, or even just pick them apart to figure out how they work in order to learn, you need to log in.
Someone correct me if I made this way more complicated than it needed to be.
As for developing a web client for theming, maybe this could be a community-led effort? I don't have the skill or time to do any of it, but if this is a popular request, perhaps we could organize a project and try to contribute to it. Is anyone interested?