Robb:

What I'm about to suggest is probably a sacrilege to devoted electric players but ...

I have a Strat that I primarily use as a midi controller, but when I want to play it as an electric I run it through my Digitch RP355 and listen through headphones.
http://www.sweetwater.com/store/detail/RP355/

It has 34 amp models, 18 cabinet models plus effects and a WAH pedal - and you can use the audio outs to record in a DAW.
You can also save 70 presets of your own.
Not exactly what you asked for but obviously is very quiet and very flexible for tone.

John