Reason does support audio input, but in a very limited way.
You have to use the Rebirth Input Machine. I haven't seen any software use this directly, but if you use the ASIO4ALL driver for audio, it pipes the audio input into the ReBirth Input Machine. I've been using the vocoder this way for years, and it works well. The downside is that you are using ASIO4ALL rather than the native driver, which won't provide the same low-latency performance, but close depending on the card.
I talked to a Propellerheads rep once about their lack of support for VSTs. They don't support VSTs and what not because they don't want to provide tech support interfacing with buggy and problematic VST plugins, and then get blamed for crashes that are primarily a VST issue.
Anyway, I think the real solution to your problem is to use Record with Reason. It allows you to work with audio inputs, and you could run the outs from one program to Record/Reason. Since you already own Reason, the upgrade isn't too expensive. Last I checked, $100 or so.