The question is: What will work best to purge an LP tank. i.e. Displace Gasified Propane?
Cutting into a LP/Propane tank has HUGE RISK! Extreme CAUTION must be employeed! Use an Explosive Level meter to ensure safety!
There is a thread from RCWelding (07-10-2010) with much discussion on this subject.
I did not find any of the following important information in that discussion. Using Dawn soap is discussed in his thread & is warranted.

The question is: What will work best to displace Gasified Propane?
Something to consider in trying to displace Gasified Propane.
Molecular Weights of the fuels/gasses in the discussion by lightest to heaviest.
CO (Pure Carbon Monoxide)        28.011
CO (Exhaust/Impure CO)             28.011+ (unknown wt.)
N3 (Nitrogen)                                28.013
Air (common blend of gasses)     28.966
AR (Argon)                                   39.948
CO2 (Carbon Dioxide)                 44.010
C3H8 (Gasified Propane)            44.097

As you can see the Gasified Propane is the heaviest of all of them with CO being the lightest.
If you are trying to displace the propane gasses the openings MUST BE ON THE BOTTOM/FACING DOWN to allow the volatile gasses to escape.
If you are purging the tank and the openings are anywhere other than on the bottom you are asking for serious trouble!
None of the lighter gasses can blend with or move the very HEAVY Gasified Propane uphill to an opening above the bottom.

YES - CO2 will mix fairly well with the Gasified Propane but only close to 50% dilution at best. Don't chance it!  
CO & N3 will "push" the Gasified Propane out the bottom better than any of the others as they are the lightest.
Using "Exhaust" is quite hazardous as it has unburned oxygen/fuel components within the "Impure" Carbon Monoxide, nullifying the safety factor.
Accordingly - N3 (Nitrogen) is the best purging gas as it is very light and has NO OXYGEN or Fuel component! BUT, the openings MUST be facing down!

Source: http://www.stadealer.com/uploads/1/8/4/1/18412059/coalarminstallationheight.pdf