A hotel in Takayama for Spring Festival

I am planning to stay two nights: April 14 & 15 2018 in the town of Takayama for the spring Festival. Unfortunately I can't find a hotel or a Ryokan for these dates in the town of Takayama. Everything is fully booked. Do you have any suggestion how I can make it to the Festival? Is there an overnight train from Takayama to nearby towns, so I can be at the Festival on the night of April 14th, and take a late night train to a hotel in a town nearby?

Expect all forms of transportation to be jam packed also.

Have you tried Hotel Associa? It's a little out of town but walkable, and it is awesome there

If it doesn't need to be a hotel specifically you could consider staying at a hostel.
I went to Takayama festival last spring and stayed at K's House Takayama. It was quite expensive for a hostel during the festival period but it was really nice and in a great location. They have two properties in Takayama (the second is calked K's House Oasis) but I don't know what the other one is like. There are other hostels in Takayama too such as J Hoppers.

Also, having read a lot about the festival I expected if to be incredibly busy but it really wasn't at all. Perhaps because the cherry blossom was a bit late last year. Anyway, we had a lovely time in Takayama and it was one of our favourite places we visited during this trip. It's a great base for visiting Shirakawago too which I would recommend.

Hope you find somewhere to stay and enjoy the festival!