To start: I am a property manager, never managed 30x doors remotely. Goes with the job, I live and work in the territory I work in.
The following things I believe to be true: you could definitely do this; you will definitely take on more risk.
Food for thought: building a strong network of folks you trust would be a must. For sure. By virtue of asking this here, it's clear you're weighing the benefits (feasibility) of doing it yourself or hiring someone. Keep in mind...though you might have a strong network of trust between agents and vendors, that does not equate to a signed property management agreement where the PM is contractually obligated to take care of your portfolio. Read: the trust of the agents and contractors you work with will go so far as their good will does. If you sign a contract with compensation for these agents and vendors to assist your portfolio....well, then, you've essentially done the same thing as a PM but with more contracts and relationships to manage.
Specifically answering your questions:
1. Has anyone here successfully managed a portfolio of this size
remotely? Never managed remotely.
2. What advice do you have for establishing a reliable local network
when you're not physically in the area? What other resources such as VA's could I consider? Referrals from local PMs would be a good start. If you don't want to "get sold" by a PM when you're really looking for vendors, then talk to brokers on the buy/sell side instead. I see you're a broker too, so you have your cleaners, other agents to show properties etc.
Virtual Assistants: VPM Solutions is a company that specifically trains and sources VAs for property management. Would be a good start.
3. At what point would you consider relocating to be a necessary or advantageous move?(number of doors) Don't know about relocating, however, the adage is 50x doors per PM. That's with them running everything. Maintenance coordination, leasing, etc. With that said, if you search the forums here you will see folks managing 100, 200+ doors with a small team to assist (showing agents, maintenance, etc.) Doesn't answer your specific question above but worth adding.
4. Are there specific tools or systems that you recommend for remote management that could help streamline operations? There are tons of software to choose from. I'm sure folks will respond here with the list of them. If you're managing remotely, then finding a software that enables remote showings (if you don't have someone on the ground to show it for you) and you can advertise/screen/place folks from it. All the big software companies (RentVine, Buildium, AppFolio, on and on...) have capabilities like this. I use ShowMojo for my remote showings and screenings and it gets the job done.
Sidenote: I'm in Tacoma if you want to shoot the breeze and talk about this more. Don't know where you're at in WA.