Philpot, I don't know how this one slipped by in February, but you have the compressibility thing all wrong.
Once you have done the IAS to TAS calculation the next step, calculating the compressibilty correction finds the correct TAS, not EAS. In your example the first calculation gives you the false, high, TAS. It is false and high because you have not allowed for compressibilty raising the air density. Now you check for this effect and find out the true TAS.
Check the lttle table in Bristol notes that shows how you move between IAS/CAS, EAS and TAS
Dick W