Having just gone through this, I saved the HTML you get when entering a new round, and propose to do the following
Property: lastColosseumRoundWon
Set to 0 when you ascend
Set to (current round - 1) when you start a battle, based on text
Incremented when you win
When you are about to enter the Colosseum in the Relay Browser, if lastColosseumRoundWon < 15, figure out which weapon is "best" - dragnet, switchblade, dodgeball - and if you do not have it equipped, put up a warning screen of the sort used for saving kung-fu buffs, 100% familiar runs, and so on: suggest that you equip the "best" weapon, click on left image to do it, click on right image to proceed anyway.
I've been equipping weapons in the CLI, cycling through them, but there were several rounds where I forgot to do that and was surprised when the opponent did a special move and I did not have the correct counter available, since I didn't have the right weapon equipped.
I will not ascend today; I want to get the arena parameters of the feral kobold and the reanimated reanimator, which will take most of tomorrow's turns, but I will ascend tomorrow and be back to the Colosseum on Sunday.