Chasing in is the first option I would use, you may as well learn some basic plastering skills as they will come in handy, saved me a fortune over the years.
You can also get quadrant trunking which blends in better with skirting boards.
Sounds like hard work but lift the floor boards and identify the correct cables then wire it so you maintain the ring circuit, better to do the job properly the first time. If your lucky the joists will be running the right way, if not refer to the OSG and start notching out as required. Remember to avoid putting cables close to heating pipes etc and derate the cable as applicable for your fixing method.
Rather than a quick fix, do it properly and you will learn time appreciation for a job and how to overcome problems without the customer looking over your shoulder. Just send your missus shopping until the works done.