I did see huge variations in cost from different vendors around town.  

It could be a variety of reasons which you have not stated, and any of the variations on that reason could be true or dubious, but in the end there are very few sellers who will part with significant potential gains to save on improvements or the time it would take to turn around a property when they themselves have the means to carryback the financing. 

I have tried different variations of the term "webuyhouses", "webuyhomes", "cashforhouses" and so on.

I already know the answer is yes but let's evaluate, discuss and see how many variations of a workable solution we can create. 

There is risk, variation of income, and all kinds of other things to worry about.Do you "live the dream" and travel/vacation year round, do you focus on building your empire to ever greater heights, or do you pursue some other passion? 

The calls I made started taking their own path, til finally I realized that all I need to do is introduce myself, tell them what made me call and let them know I was interested in buying their house followed by asking them any variation of 2 questions...#1 are you interesting in selling?

As for investment property, there are all sorts of variations based on homestead exemptions.

Some companies are more lenient on certain type of  products (OO vs. rentals and some other variations) .  

We made do with a variation that was not our first choice, but that works just fine.

Any suggestions on how to account for contractor to contractor pricing variation?