I only mention this because I noticed your mention of Furnished Finder, which is the only platform I list my MTR, and FF caters to 30+ day stays. 

Most serious and qualified tenants are searching on the major 3rd party platforms you mentioned + realtor.com, redfin, and a few others.Apartments.com & homes.com are owned by the same company and may offer some additional marketing options.Another strategy to consider here is social media - video marketing.

The trust one can build up over the years on platforms like BP, Youtube and others is insane.

These things need so much power that unless the site has access to major grid access point you're wasting your time. 

You can't even access his BP podcast any more.

They often have access to off-market listings and can also help you navigate on-market listings on MLS.

Most Buyers don't even know that there is a public access portal to search local listings.

while still trying to keep up with the competition Do you rely more on direct-to-seller marketing, networking with agents, leveraging platforms like PropStream and Batch Leads, or just by looking at a lot of deals?

The agent will have access to the biggest platform to get the property sold though, the MLS, so forgoing even a cut rate agent will create more of a loss than the agent fees themselves. 

Also leveraging platforms like PropStream and Batch Leads are excellent strategies for building a solid buyer list.