Can you assume atmosphere height for the purpose of surface pressure calculation? Given that by definition of scale height an atmosphere thins by a factor of 1/e^x where x is elevation in terms of scale height multiples (See the table here: Definition of Scale Height), can we assume that the atmosphere is effectively non-existent at the elevation of 6H?

Density at elevation 6H
1/e^6 = ~0.00248 would mean about 0.2% of density at surface level

I know there is no real physical boundary but what I'm looking for is what is the assumed standard for simplifying calculations. Or is it just a bad idea to try and do it this way?

*This is a followup to another question:
How can you determine the initial volume of a planet's atmosphere?
It all depends on what you are trying to do. For some purposes 6H might correspond to an adequate vacuum  for others not. The density is not low enough to ignore its effects on a space craft (we are talking of $\approx 48$ km in the case of the Earth). Indeed $48$km is less than the altitude record for an unmanned balloon, though greater than the altitude records for air breathing aircraft.