Number 1 is what we did with Sleepy and Kukawaki a while back and it worked really well. We hit him hard at first to trigger the first mines as close to the start of the encounter as possible (to avoid Skolas Transmitted Disease swap fatigue), started running around the arena to set up then burned him before taking care of the mines.
Just bear in mind that the mines don't dissappear once Skolas is dead.
I hate the all or nothing strategies, people try them without the right amount of firepower and/or coordination and wipe more often than not. It's part of what sent DGAF into a hate spiral with HM Crota trying to beat him before ogres.
The mines are an easy section if you don't panic and have great teamwork, it's OK for people to die and sometimes it even makes sense to let the buff kill someone during that phase. On all the Skolas School kills we had with first timers we beat it every time we made it to the second mine round without burning him down. We handled the mines, regrouped, then killed him. Some teams died on the first round just figuring out what was going on but the burn strategy is tough to recover from if you don't pull it off.
It takes 5 minutes longer but has a much higher success rate IMO