I had actually considered redoing this run myself, but I haven't had a lot of free time as of late.
I don't think that there's any problem with naming the hero 'EEE'. I had been considering using the name 'I', because it flows well in the dialogue; 'I defeated so-and-so', etc. For choosing a rival name, I would probably use pokémon blue, and choose the name 'ASH'. It's around 65 frames slower than using a one character name, but still 77 frames faster than what I did, which I think is a reasonable stylistic choice. Don't forget that you can exit the name screens with the start button (for pokémon as well).
Further analysis. Also note the bit about switching attacks.
I also made a route mistake just before Bill's. The Hiker with four pokémon is avoidable, and you can fight the Jr. Trainer above him instead which only has two. This will also give you two extra Bubblebeams to work with, which means you can avoid using Hydro Pump for the rival's Pigeotto on SS Anne (Hydro Pump has an 'no-animation animation' which is 55 frames slower than most other attacks, so it's best to avoid using it).
How 'difficult' a pokémon is to catch is independent of their level. I know from experience that a Snorlax can be caught with just a plain poké ball. When will you be catching Snorlax exactly? There are a few sections that you could probably avoid doing with Gyarados, and then do later with Snorlax. Celedon Gym comes to mind, and of course the Silphco. Building.
A L132 Snorlax should have an openning moveset of Body Slam, Harden, Double-Edge, and Hyper Beam. Harden is worthless, and Double-Edge can't be used if you intend to do a no damage run. For a third attack, Rock Slide might be a good choice, mainly for the ghosts. It's a normal attack (as opposed to special), which means it will utilize Snorlax's high attack, and it won't produce a 'super effective' message as Earthquake or Psychic would. The fourth attack could be Surf or Ice Beam. I think the Veridian Gym will require one of the two. Surf seems like a better choice, because it's just as powerful, and it has more PP.
I like the idea, and I think it could be a good run. Good Luck :)