I wanted to let you know I tried working with your approach and it worked. However, sound quality and latencies were quite poor with my notebook hardware. Spent several hours playing with the ASIO4ALL driver, which assures good sound quality and latency, but for the price of making the sound device unavailable for other applications. This seems to be by design and explains, why the web browser sound stops working as soon as I run the virtual amp application (both as standalone or VST in Reaper). I purchased a 10€ USB sound card in order to have a 2nd device available, which turned out to be quite complicated to setup and made me drift away from my initial goal to have a setup as simple as possible.
This is why I decided to stop wasting time trying to mix the sound of web browser and guitar on the computer. Now I use a cable more than initially wanted and hook up the computer to to the AUX input of my KORG Pandora 4XD. That works fine now.
Again, I appreciate you contribution !