I'm pretty sure you can get that package (in the office behind the desk) before G-spotlight--I think the doors are open before then but I could be wrong.
As far as the mission, try to be methodical, if you are having trouble with just the one pair or way points, I'd do it first and get it out of the way-- I really don't remember it being real hard after I got the hang of flying the plane. I think it took me 3 or 4 tries. Of course that was 10 months ago.
This is the text of a strategy that I just got of gamefaqs.com-- I don't know how effective it is though. I would use the strategy below and make sure you pause and look at your map and this guide so you line up your runs for each one correctly.
Here it is:
Strategy: Although the checkpoints can be obtained in any order, if you get them using the following sequence, you will be able to fly a circular pattern around the city and eliminate the need to reverse direction to get the next checkpoint.
Once you are airborne, begin flying west to the starting checkpoint in the center of Downtown (1). (Note: This is NOT the checkpoint immediately to the west when you start!) Ideally, you should approach this checkpoint from the north and be traveling south. However, you can also approach it from the east and be traveling west, but this direction will require you to make a hard left turn after reaching the checkpoint in order to avoid crashing into a building.
Fly south to the ending checkpoint that is in the center of Little Haiti. The next starting checkpoint is located south of the previous ending checkpoint in the southwest part of Little Haiti (2). The ending checkpoint is above the Escobar International Airport terminal entrance. After reaching the ending checkpoint, fly east to the next starting checkpoint over the docks in Vice Port (3). The ending checkpoint is in the eastern part of Little Haiti near the bridge to Starfish Island. Once the ending checkpoint is reached, the next starting checkpoint is located directly to the north of the previous ending checkpoint (4). The ending checkpoint is between two buildings in Little Haiti. You will need to approach the ending checkpoint from the west, traveling east in order to line up with it and avoid crashing into one of the buildings. The next checkpoint is located in the northeast part of Downtown (5) and its ending checkpoint is immediately west of the bridge leading to Prawn Island. The final starting checkpoint is located in north Downtown above the dirt bike track (6). The final ending checkpoint is located in the west part of Downtown.
Tip: The plane controls are quite sensitive. Always keep the accelerator button pressed to maintain your airspeed or the plane will start to descend.