If I would have a shop that does this kind of work, I would charge just the labor, since there aren't any components to replace.
Unfortunately, nobody is in the repair business anymore today!
But, if you find a shop, I would estimate an hour for the reflow. In the US it probably would cost you $75-$125 to do it.
Downside, there may be components damaged and to troubleshoot, find and replace them it would take more time and material.
I would look around with my friends, perhaps there is someone that knows how to solder?