You must have either Caterpie/Weedle or Koffing+Cubone to go for this strat.  This strat allows skipping Pidgeotto/Tangela grass, and instead going to the grass where you catch Spearow between LG-Fly rounds.

After Celadon OWRB, inside Pokemon center:
 - Swap Burn Heal with Coin Case
 - Swap PokeFlute with Old Amber
 - Swap Roaming TMs with warping, toss 38
 - Scroll down 3 places to New Name
 - Exit Pokemon Center and warp to Seafoam
 - Go down first ladder, immediately get on bike at cursor position
 - Jack to ladder after catching Psyduck + Seel
 - Catch Staryu + Krabby, jack to Articuno
 - After Articuno, swap Burn Heal with 8 8, Dig out

 - Change to Box 3 afterwards and continue into Mewtwo Cave like normal
 - If you got a bug, you must catch Chansey or do Rhyhorn CT
 - If you got Koffing, catching Chansey requires Venonat LG-Fly

 - Continue normally up until LG-Fly Round 1.

LG-Fly Round 1:
177 Squirtle
    Rhyhorn 4848
176 Charmander
157 Goldeen
    Ditto FF
 72 Jynx
    Scyther 4848
150 Pidgeotto
149 Alakazam (9F 17 times)
    Shellder 4848
126 Machamp
    CONTINUE WITH EITHER BUG OR KOFFING BELOW

Bug:
112 Weedle (or 123 Caterpie)
108 Ekans
100 Jigglypuff
    Lapras 4848

Koffing:
123 Caterpie
112 Weedle 
108 Ekans
    Lickitung 4848

 - After Round 1, Fly to Celadon
 - Bike to Game Corner, get Pokemon there
 - Before exiting, open menu
 - Evolve Pokemon in party
 - Swap PokeFlute with Moon Stonex10
 - Move cursor up to GlitchItemx23 below brightness Ultra Balls
 - Exit Game Corner, get on Bicycle at cursor position
 - Bike to this tile:  http://puu.sh/ilFiC/7833e7c3ba.jpg
 - Go 5 tiles up and 1 tile left from that position, open menu (facing left)
 - Scroll up to Cancel, use it
 - Scroll down to Burn Healx0, use one on Ditto
 - Close menu and bike to Snorlax (down 1 then straight left, jack into tree)
 - Swap Ditto to front of party
 - Scroll down to the PokeFlute you swapped down earlier, use it
 - Wake up Snorlax, set up CT, then catch it
 - Go straight up into Fly grass
 - Catch Spearow and Rattata (Doduo if you still need it)
 - Fly to Saffron and set up LG-Fly Round 2

Bug:
 71 Poliwag
 64 Farfetch'd
 57 Mankey
 55 Koffing
    Cubone 4848
 53 Electabuzz
    Tauros (9F 15 times)
    Exeggcute 4848
 51 Magmar
 37 Slowpoke
 30 Tangela
 24 Tentacool
  9 Ivysaur
  3 Nidoran Male
    Lickitung 4848

Koffing:
 71 Poliwag
*65 Venonat
 64 Farfetch'd
 57 Mankey
 53 Electabuzz
 51 Magmar
*40 Chansey
    Tauros (9F 15 times)
    Exeggcute 4848
 37 Slowpoke
 30 Tangela
 24 Tentacool
  9 Ivysaur
  3 Nidoran Male
100 Jigglypuff
    Lapras 4848

* - CHOOSE ONLY ONE

Advantages:
 - Skip Pidgeotto/Tangela Dsum
 - Skip 3-5 Rare candies on Pidgeotto, no longer considered for OWRB
 - CT always gets set up without an extra encounter
 - Less movement overall (not yet tested)
 - Initial Burn Heal buy can be changed to something else
 - You can group 3 Moon stone evolutions together on Bug strats

Disadvantages:
 - Rattata may be level 18 which requires 2 candies
 - Requires an extra use of Cancel in Seafoam
 - Slightly more menuing overall
 - You have to release 2-4 Pokemon before Round 2 for box space

Other Notes:
 - If doing Rhyhorn CT, you can 4848 Exeggcute in Round 1 after Caterpie/Weedle
 - This allows room for Venonat/Chansey/NidoranF (15) in Round 2