What size CPU and RAM do I need to run a node of your branch? Would it be feasible to run on a VPS server (i.e. one with the space necessary to hold the blockchain)?
The most recent version of 1mb_segwit needs about half as much RAM but a little more CPU than p2pool master.
If you're using pypy, you should probably have about 3-4 GB of available RAM and a 2.2 GHz Intel Core-based CPU or better. AMD Ryzen CPUs should work fine. Older AMD CPUs (e.g. A10 or A8) will need a lot more GHz, but if you have a 3.5 GHz older AMD CPU, that will probably also work fine. You might be able to get away with slower CPUs, but I can't promise anything.
If you're using python2.7, then you only need about 1.5 GB of available RAM but you might need a 3.0 GHz Intel Core i3 CPU.
I strongly recommend using pypy. That's much easier to do on Linux. Orphan rates will be lower and revenue will be higher if you use a fast CPU and if you use pypy.
Thread and core counts are basically irrelevant. GHz and IPC are king. This means a cheap desktop Core i3 CPU will be quite a bit better than a high-end server 16-core Xeon. The Xeon should still work fine, though.
Unfortunately, p2pool requires that the full node's blockchain be unpruned. It needs to access the genesis block for some reason; I haven't looked into the details on why. I recommend making the ~/.bitcoin/blocks/ directory a symlink to a cheap HDD and keeping the ~/.bitcoin/chainstate/ directory on an SSD. The chainstate is the UTXO database, and it needs to be read from and written to frequently and randomly when validating blocks. The blocks directory is just the raw block storage, and is accessed infrequently and sequentially, which makes it perfect for HDDs.