Robert,
If the largest error comes from the baro correction on the ground, why not use all radio-based aids? My previous post just pointed out that all "new advanced aircraft" will have (at least) one radio altimeter and (at least) one GPS - soon to be updated if the GA market is anything to go by to WAAS-capable units that provide accurate altitudes above ground level irrespective of baro pressure measurement or temperature effects. I appreciate that the modern Air Data Computer also provides extremely accurate local pressure measurement but it is only as good as that taken at the ground and worse if there is any appreciable delay since that reading (& the temperature if cold) was taken & transmitted to the aircrew.