If you're parking for many minutes and have NO COVER you did it wrong. Period. The base should be SHUT DOWN, nobody should be left alive to hunt you down, and you should be over the town with at least 6 fighters covering you as you drop your troops.
Quit screwing around with the goonie bird and maybe you'll be less frustrated.
Also, you can spot a bloody C-47 miles away! Even outside icon range you can sometimes tell what it is from the shape of the wings alone. Seeing one parked on the ground isn't all that hard. If a plane 8k out sees something and heads that way to investigate, and finds you, well golly gee, of COURSE it's going to look like he came straight to you! He's not going to fly over you, say "Yep, that's an enemy goon" and then leave you alone!
Silly mortal!