Them Gentlemen will be the death of me... Also my horrible luck with Mt Moon & the RNG...
Anyway, I went for a more speedy route & aimed for the HP Up on Route 2. Basically I followed the standard speed-run route all the way to Mt. Moon (stocking up on a couple of Poké Balls, Potions, & Antidotes), before making deviations at Mt. Moon. First to get the Water Gun TM, next to get the HP Up at the end of the first ladder, then continuing as normal, getting Mega Punch, etc. I also caught a Paras along the way because it was necessary for the strat. At Cerulean, I followed the standard route (getting Whirlwind & selling), before beating Misty & teaching Bubblebeam. I then went up Nugget Bridge, got the Nugget, TM45 (I forget what it contains), then zipping to Bill (Deviating to beat a trainer to get Seismic Toss). Following that, I beat the Rocket with Dig (To sell), then zip-lined along the main route. At this point it was like 6-7 minutes to go so I needed to hurry on a lot. I beat the rival, got Cut to teach to Paras, then rushed out, waiting for S.S. Anne to part, then buying a Repel to rush through Diglett's Cave (no wilds), get the HP Up on Route 2, & selling in Viridian before calling it at the 59 minute mark.
If my luck was not so terrible (I can recall 17 wild encounters on Mt. Moon) I would have beaten a couple of Gentlemen, but... >_>
Grats Jimera0, you deserved it in the end (either you or Mekkah), but yeah. Gentlemen >>>>>>>>>>> Getting a HP Up on Route 2.
It was a second attempt, my submission.