Does anybody have experience with huge number of partitions if so where did you start running into trouble?
I use an arbitrary 100-way split for a lot of tracking info. Just modulo 100 on the ID column. I've never had any issues with that. If you can adjust your queries to pick the right partition ahead of time, which I am able to do for many queries, the number of partitions shouldn't matter much. Only rarely do I need to query the primary table.
I don't think your plan for 365 partitions is outrageous on modern large hardware. For 1000 partitions, I don't know. It will depend on how you can optimize your queries before giving them to postgres.
