What I don't know is what the weather is like in late December in that region. I do know that the bus route from Shirahama to Kyyasan is closed during the winter. Here is the link to the Kansai Wakayama Pass, which includes a bi-lingual bus schedule.
http://www.kumano-travel.com/index/en/action_ContentsDetail_Detail/id1...A two day pass is 3500, and your should be able to take the bus to Yunomine Onsen, and other places near Hongu Taisha on the first day. (Route 1, Shirahama to Hongu area)
On the second day, the earliest bus leaves Yunomine Onsen at 6:55 AM, and arrives at Shingu Station at 8:05 AM. The next train to Kumanoshi Station is a limited Express that leaves at 9:13. The next Kisei liner train leaves at 10:52.
I am not sure how much time you plan to spend on the shoreline, or, the amount of time you plan to spend at Magose Pass, but if you spend over an hour at each, you will probably not be able to make it to Kyoto that night.
You will also be storing your luggage in lockers at Kumanoshi and Owase, and I can't promise that there will be one available.
I believe that the second day will be too diffucult to do.
I would be tempted to tell you to get a hotel the second day in Katsuura, drop off your luggage, and then go to Kumanoshi and Owase before returning to Katsuura. The bus pass will get you on a bus to Katsuura.
There is easy train access to Kyoto from Katsuura. There is a limited express train to Shin-Osaka Station, and then either Shinkansen or a rapid service to Kyoto. The lower cost is 7440 yen (rapid service), which is less than a 4 day JR Kansai Wide Area Pass (7000 yen). Link to the Pass:
http://www.japan-guide.com/e/e2361_08.htmlThe pass stops at Shingu, and does not cover trains to Komanoshi or Owase. But you may be ab le to use the JR pass the following three days.
I think you should concider this a three day trip, and I hope I have given you the information to confirm this.
I hope this helps.
