Even on Earth they resort to shipping cases of hard drives instead of transferring over the Internet.
One technique where simply waiting 6 months works very well is in measuring parallax. The Gaia spacecraft takes advantage of this.
But I'm optimistic that some institutions (hopefully including mine!) will be able to transfer these data over the network after the next run of EHT observations. Exciting stuff for sure.
I wish I could shed some more light on the ins-and-outs of exactly how these observations work, but I just run the computers, man. :) What I can tell you is that in order to move data off of the collector machines, they typically use m5copy, which is a part of the JIVE project (they have a Github repo: https://github.com/jive-vlbi/jive5ab). All communication between the control computer and the collectors happens within a private, physically-distinct network, but it's just standard commodity networking equipment between the control computer and the collectors. The folks in charge of the node's design are in the process of removing some of the bottlenecks to make electronic transfers more viable (the current spec doesn't even include a 10Gbps uplink!).
Space-based very long baseline interferometry (VLBI) has been done at lower frequencies, most recently with the RadioAstron satellite[0]. There hasn't yet been a VLBI satellite observing at the same frequencies that the EHT uses, but there are mission concepts being discussed. [1] discusses some of the technical challenges.
(1) https://www.smbc-comics.com/comic/delta-v
edit: We could also send the (super)computer that will process these images in LEO, so we don't even have to worry about atmospheric re-entry.
Would it be possible to use the same trick in space? IE: get a baseline the diameter of Earth's orbit (roughly)?