Stellar's making me post this, I'll spare you guys the indepth.
I started my run at 3:35 with Totodile aiming for it to be morning after the defeat of Falkner. In hindsight it would've been better to try and run for nighttime Ilex like some of the other folks here. I would grab Poliwag/Spinarak/Gastly then once day hit would pop into Dark Cave to grab Zubat/Geodude and hope for a Teddiursa (I never found one...). I'd do standard speedrun up to Goldenrod then hang around that area for the last 10 or so minutes.
I only used Toto as the main damage dealer in the run, with very occasional use of Gastly for Hypnosis and other 'mons for bringing down hp for catching.
My catch list: Totodile, Croconaw, Spinarak, Poliwag, Gastly, Togepi, Bellsprout, Onix(trade), Spearow(gift), Sandshrew, Magikarp, Goldeen, Ekans, Rattata, Hoppip, Caterpie, Pidgey, Zubat, Geodude, Krabby, Snubbull, Exeggcute, Hoothoot, NidoranM, NidoranF, Jigglypuff, Metapod, Noctowl, Pineco, Paras, Weedle, Ledyba.