Altering the tyre pressure won't have a great deal of difference now, only a little bit of less drag. Your Power tap P1 is providing the correct power figure, so Bkool can work with accuracy.
When using Bkool Pro, it guesses the power from rotational speed of the flywheel. So by reducing drag to a minimum and then quickly spinning up the flywheel using a high cadence, a huge power number is produced. If you're reasonably strong, you can get ontop of this wave of power and just keep pushing it along. Result is, small short inclines flatten, Bkool SIM reacts too slow to add resistance, when it it does eventually add resistance, you've powered over the incline and are now on the descent, resistance eases again. On flat courses I could use a 53 crank,11cog at over 100rpm cadence for an hour. This would give me an average of over 400W.