Not sure if this is known, and it isn't really useful as far as I can tell, but it might inspire some ideas.

By starting a Grenade Rampage and exploding a few vehicles, they can explode again during a replay (as long as the replay is long enough, in the video I fail to get a long enough replay twice). If the rampage ends during the replay, the game gives you (30000 - the number of grenades you used) grenades

^That partial teleport could be useful to teleport back to Kaufman Cabs after Taxi 2

After throwing the grenade, run between the tree and the wall at a specific angle to clip through the wall. After the kill, grab the Quad bike, or buy the Quad if it got destroyed.

The dock teleport also works on PS2, and it can lead to two locations: Leaf Links and the roof of a house near Lance, as marked by the image

Potential Reroute:

Left side of the image is old/suggested route, middle are the routes with the between-mission drives, right side are the relevant drives (the ones that are different)

Difference maps (red is old route, purple is new route):

After Home's on the Range+Deathwarp (timed with Ambulance) Time (old): 29.67 Time (new): 16.54

After Purple Haze (timed with Oceanic) Time (old): 1:42.22 Time (new): 44.40

After Where it Hurts The Most (timed with Sentinel) Time (old): 55.59 (-7~ seconds from loading screen) Time (new): 31.83

After Kill Pill: Part II (Timed with Sanchez) Time (old): 1:23.18 Time (new): 38.97

After High Wire (Timed with Maverick) Time (old): 26.97 Time (new): 37.21

Total Time (old): 5:14.22 Total Time (new): 2:48.95

Time gained: 2:25.27

Slight timing errors aside, the suggested route improves the route by at least 2 minutes.

This new route is already on the document, on the "Potential Re-routes" tab.