Festival light sculpture LED power question
The way you have proposed setting it up should be fine.

The lights take a 31V input, multiple chains are set up in parallel (despite appearances) so increasing the length increases the current draw.

The total load for 1800 lights should be a bit over 1 amp. So you can get a rough idea of your running time by looking at the amp-hour figure of your battery. Don't cut it fine, batteries can be combined by connecting them in parallel.

It may be possible to run the chain on 36V using three 12V batteries in series. I would suggest testing this on a single chain, let it run for at least an hour and make sure the lights don't get too hot. However given your needs and resources the first option seems better.