The problem is that you need a simultaneous reading at both sites. Readings six or more hours apart are OK for landing aircraft (because the two humans in the front seats compensate for the inaccuracies) but probably not for your purpose. That's where your national weather bureau has a massive adva...

Pressure at Mean Sea Level is constantly varying. Your local pressures is constantly varying. The ratio between the two is constant for all sensible purposes. Would this be a more accurate way for showing the altitude then: Take the ration of your current MSL pressure, and the BMP085 measured press...