Fury From the Deep is the last Doctor Who story with all of its episodes missing. Only three serials subsequent to this one, The Wheel in Space, The Space Pirates and The Invasion have missing episodes, although the two missing parts of The Invasion have been brilliantly animated by Cosgrove Hall. I’m now on the home run! For the purposes of this marathon I viewed Loose Cannon’s superb reconstructions, links for which appear below.
Loose Cannon’s Fury From the Deep, Episode 1 Part 1
Loose Cannon’s Fury From the Deep, Episode 1 Part 2
Loose Cannon’s Fury From the Deep, Episode 2 Part 1
Loose Cannon’s Fury From the Deep, Episode 2 Part 2
Loose Cannon’s Fury From the Deep, Episode 3 Part 1
Loose Cannon’s Fury From the Deep, Episode 3 Part 2
Loose Cannon’s Fury From the Deep, Episode 4 Part 1
Loose Cannon’s Fury From the Deep, Episode 4 Part 2
Loose Cannon’s Fury From the Deep, Episode 5 Part 1
Loose Cannon’s Fury From the Deep, Episode 5 Part 2
Loose Cannon’s Fury From the Deep, Episode 6 Part 1
Loose Cannon’s Fury From the Deep, Episode 6 Part 2
The Doctor Who Mind Robber 
Actually, The Invasion is also missing two of its eight episodes, but they were so very effectively recreated via animation & the original audio soundtracks several years ago, so you can watch it from beginning to end on DVD.
You’re entirely correct. I’ve forgotten that I’ve watched The Invasion several times, complete with the animations, I guess that says a lot about how successful the animations are at recreating the lost episodes!