Well....the $15 parts trimmer lives and breathes. It appears to have had a low hours life (compared to the known hours on mine), and about the same AZ sun exposure.
It took about 4 pulls to get it to bark, and it needed some idle fiddling (someone had the idle screw backed out so it didnt contact the stop) and thus would only fast idle on the choke setting.
I'll probably pick up the special carb adjustment tool (this takes the spline version), and can then dial the high RPM to ensure it gets maxed out.
Job done...and at no cost (other than time and some frustration). Thanks all for hanging in with me.