Not sure what Bowtech has to do with this whole scenario other than a way to jab this POS dealer. If I were Bowtech, I would stay out of this feud. It is not their problem.
If I were in your situation, I would have for sure retrieved the bow after the second "wait" telling them no thanks. But, that won't happen as I own a press. My second suggestion is to pay for the work and never go back.
You can order strings on line with very quick shipping. Lots of string builders out there. The fact that this "dealer" didn't have a string on hand is a sure sign that he is incompetent or not well off enough to afford an inventory. A competent dealer can replace a string in no more than 1/2 hour including tying in the peep and nock set.