Another great free tool for HRTF-based binaural encoding is the Ambisonic Toolkit: http://www.ambisonictoolkit.net/ This is a B-format encoder/decoder: when you suggested recording 4 channels and then converting to binaural, the technology to do so is ambisonics, using a 4-channel encoding called B-format. However, I'm not sure how easy it is to manually record 4 channels and get them to translate properly to B-format. There are mics that do that. It -might- be relatively simple, but I've heard that even with the specially made soundfield mic you can run into all sorts of phase issues.
BUT: Ambisonic Toolkit will also encode a mono source, let you pan it around in 3D space, then decode to binaural.
When you install it and realise how many separate plugin components it consists of it might seem intimidating, but the documentation includes some very helpful videos that explain the workflow. You'll realise that for binaurally spatialising mono sound sources you just need a set configuration of at least 3 plugins - and you can save this as a template session in Reaper. I've used exactly this setup to do just what you're proposing - making a voice pan left to right (AND up and down and behind) in a way that puts it 'outside your own head' on headphones.
The one thing you'll notice is lacking or mismatched when working in this way is the reverb. This is especially so if your source recording is not completely dry, and its roominess/reverb is carried with it as a constant no matter where it's panned. To some extent that breaks the illusion, but it's still very good - as long as your recordings are clean.
Of course the most complete binaural image, including reverb/room response, comes from recording binaurally. But besides 3Dio/dummy head microphones you can easily do the same thing by sticking small (lav-style) omni mics directly into your own ears. I've done this with DPAs with great results.