The typical "One Call" locators will not do privately owned wires, but sure you can call them out for a service locate, then slip the guy $20 and he probably will do the locate.
I located lines for digs in order to pick up tickets for the 3rd party locators when there were no line work tickets, I absolutely would spend 30 minutes on a private locate. You get zero flags with the power company's name on it in your yard, but I'd also say that up front and it always seemed like a mutual agreement that it was understood. Keep the $20, but if I smell something on a smoker, you might as well grease the palms.
The 3rd party locators (also did that for a bit) are better at it than I was through the utility itself. They just do it more and can read into the situation, and I think that's who you get for most location calls. Staying on that a bit, if you call in and specify "electrical location only", you won't get all other utilities out there marking up the yard which could really lower the cost over a private dig ticket...less people to pay. I mean, I got electric only tickets at least. We didn't get paid much as locators and the priority were for the utility dig tickets but on slow ticket days, I'll find ya in the stack within the week. We drove all over the place, we kinda noticed "shed being built, I'll probably get a ticket there" and know the lay of the land and what who did what. Worth a shot! If it's too expensive in your mind, turn it down and I'll think of something else.
I'm assuming there's no breaks in the line as well here as the tone ends when the wire you're generating on does as well and you just lose it. However, there's hope if it's just fresh line laid (at the time) and never finalized. Private/Consumer wiring can be all over the place (freaking pools!) regardless of code. This is the same problem you'll get with those Fox and Hound tone ringers like the Fluke or Triplett found at Home Despot...when the line is broke, you lose the tone and I'll just leave a circle there in either situation. That's the point I can't complete the search. You dig that up, maybe I'll drop back by...who knows!? But when the tone is lost, that could be the end of your line very likely. Ha, unless it's lost at a garden's edge where a tiller made it fun.
And I will back the others up in that the Fluke and Triplett Fox-and-Hound locators only see about 4"...6" is being generous IMO even behind drywall. For what it's worth, I believe the ancient probe boxes we used had two of those big lantern-style 6V batteries in the source box.
And I guess my last thought on this was the guarantee of location. Ours were 1ft either left or right of the line max and it's mostly connecting the dots if it gets funky for about 10ft. Private didn't have that due to all the noise so be handy with a shovel when the lines become crosses....or whatever they do in your location. "this is my best guess" is what my crosses meant.