I've had one project where I used a custom background image for a map. In my case I was looking at how busy certain buildings on campus where throughout the day. To do this I had one table with building names and the coordinates in the image for the building. To do this, I simply created a list of the buildings and then using an image editor got the X and Y coordinates for each building. For my purpose this was close enough to what I needed so I didn't need a custom shape file to fill individual buildings. I just used color and shape to indicate the number of people. The main data table consisted of the number of people in each building at each hour of the day.
In you case, I could see one table being list of parking positions and their coordinates in the map. This would essentially move the latitude/longitude into one table and the other fields you have listed would be columns of a second table. Parking location number would be in both tables so you could join the two based on that field. I would create a calculated field to determine if the plane was "on the ground". If the time being display is greater than arrival and less than departure then it is on the ground and assumed to be at the parking position. This won't actually tack it from the runway to the parking position, but I'm not sure if that is needed. Plus you would need to know where on the map things were at each minute in order to track movement at that detail.
Hope this helps