I have just checked with the Perurail web site and they do have a train to MP on Jan 1st.
To reserve yr ticket go to orient-express.com/web/tper/tper_a2a_home.jsp
into the plan yr journey area and follow the instructions.
The MP ruins are opened to the public year round.
I suggest you stay at the Kuychi Rumi in the SV ( I own one of the houses) See many reviews on this hotel on Tripadvisor.
Claudia will arrange yr train reservations as well.