I built my own rerun team about a year ago frustrated by how everyone's gym rerun team was the same. Interesting veteran team though!
This team has served me very well and I would say it's equally as fast as the Typhlosion teams. And it's a lot cheaper because it doesn't have any rare pokemon!
https://pokepast.es/c8defe7052fc84c6
Turn 1: Bronzong + Gigalith are usually the lead. Bronzong is so bulky it never gets KO'd first round and always gets a trickroom off. Gigalith has to protect if both opponents are likely to hit it with a super effective attack, otherwise he can get some chip with rock slide or earthquake. In fire gyms you can lead togekiss allongside bronzong so it can redirect attacks.
Turn 2: Bronzong and Gigalith both explode, or if the opponent pokemon can be ko'd with another rockslide Gigalith can stay on the field.
Turn 3: Eruption/Water spout spam. Togetic is super bulky but also strong, follow me deals with priority like aqua jet on camerupt. Jellicent can get up another trickroom if things go south, octillery can heal it by clicking surf instead of water spout.