I have no knowledge of how the regulatory funding mechanism works for US utilities, but I can say from experience that the UK regulator really does push for networks to find the minimum cost solution.
There are other measures that can be taken before restringing. At a high level, these are the things that can be done to alleviate an overhead line constraint:
* Are there any viable operational mitigations - i.e., can the normal running arrangement of the network be modified, such as transferring load on to another substation?
* Are flexibility/demand response services an option?
* Line reprofiling (changing fittings on towers, clearing vegetation) to run the line at a higher temperature