It sounds like you'd want puppet bridges. Each of your conversations on the remote side has a corresponding room, and what you say in that room is forwarded by the bridge trough your remote account.

You could try out dendrite.matrix.org as a homeserver (btw, dendrite would nicely fit into these 4GB). Most bridges need admin access to the server though, if you want to host them yourself. t2bot.io hosts a few you'd be able to use with your own dendrite, though it hits capacity problems at times.

Finally, you could try to make synapse leaner by not joining big rooms with hundreds of federating servers. There is a max_complexity (something like it) setting for that use case.