Doesn't look promising.
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Would echo, system lord, with some wrinkles.
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One big session
every 4 minutes eliminate last 2 on leaderboard
no pit stop, pulling into the pits or shopping/crashing on circuit drops you out at whatever the next elimination position is.
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This would mean that in order to get pole you would need to stay out of the elimination zone fir the entire session.
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As you have to be fuelled and tyred for the whole session your early lap times will be impaired preventing a one shot lap early on.
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The pole winner is likely to have to do several "hot" laps thought the session as times increase.
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The 4 minute counter gives anyone who is in the elimination zone (i.e. last 2 on leaderboard) long enough to get a hot lap in to try to get out, and anyone else close to the zone will also have to push just in case they get dropped in at the last moment.