If for some reason the SDK option does not works for you;
Another option might be Logic League, especially if you expect to continue using P6. Of course, this is at extra cost and you must verify compatibility with your version of P6 and what when newer versions arrive. It is better when the software gives you direct access to the links table as a few others do.
http://www.scheduleanalyzer.com/ll_brochure.htm
Another option to explore if you have Primavera Risk is to check if there you have access to the links table as it being so expensive I suppose it must give access to the links table, then make the changes in Primavera Risk and import the job back into P6.
Do not forget about lag values, that will usually 0 on FS links, here another global change on the links table would help if you have access to the table. The change might be drastic depending on the model so in order to meet deadlines some duration chages and activity splitting might be needed as to recover some of the overlapping. Just a reminder as I believe you are aware of these details.
Good luck,
Rafael