Because of a re-arrangement in the kitchen, the sink will now have to
be on a wall that, due to frameing and very limited space, will not
permit a direct vent through the roof in that location. So, the only
alternative I can think of is to run a separate vent pipe from under
the house as shown in the picture he
http://img.photobucket.com/albums/v4...lternative.jpg

Is this a viable alternative, or is there a better or more effective
way? Can I just run the drain into the waste/vent stack without the
additional pipe for venting? Advice would be appreciated.

Look at Studor Vents.
(air admittance device)
TB

Great Suggestion!! Thanks for the heads-up!!