Calculating takeoff performance in high mountainous airports

For example, Leadville sits at 9934ft elevation. The takeoff performance chart for the C172S only goes up to a pressure altitude of 8000ft. Essentially, if you’re trying to fly out of Leadville, your numbers go off the chart. 

91.103 says we need takeoff data but we can’t get it…. So does this make Leadville “legally” inaccessible for a 172?

Or, is it legal/accurate to compare density altitudes?

For example, if KLXV weather was currently 

Baro 30.45 and Temp of 17c, then Density Altitude is ~ 12000ft. 

Likewise, if we hypothetically just use 8000ft Pressure Altitude but plug in 33c into an electronic E6B, we also get 12000ft Density Altitude. 

Does this mean we can use the takeoff chart in the 172s POH by finding the data for a hypothetical airport at 8000ft PA with a temperature of 33c to find our ground roll in Leadville?

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