I tried just blowing up all the cars during Rush Hour (instead of just the last one) and while the rental-car guy complains about it, the mission seems to be the same otherwise (you have to get to all the cars anyway). The only downside seems to be that the police can bother you more when you blow stuff up.

Now doing Riding Shotgun before this mission gives you a lot of machine gun ammo, which allows you to get the cars to stop quickly (or just ram into them if you're car health allows it). You can then either use a machine gun to blow them up, or use the RPG once the rental car is stationary (which allows you to hit it easily as opposed to a moving target where you can sometimes waste a lot of rockets on it).

Comparing to the mission in zoton2's 2:03:04 WR (which seemed pretty solid), I was already ahead 20 seconds after the second car with using the RPG to blow the rental cars up after they stopped. I caught up with the third car at the beginning of the bridge and then turned around and went after the fourth car instead of driving to the other island and towards it. I caught up with the fourth car roughly when it turned onto the bridge where you would otherwise usually meet it on, which was about 18 seconds before zoton met up with the fourth car. Maybe another car order would be faster or maybe doing the usual route instead of trying to catch up with the fourth car, but I'm not sure. With better driving (I had some crashes) it would probably be even a bit faster.

It took zoton over 20 seconds to blow up the last car (understandable having only a pistol), so having loads of machine gun ammo at this point also helps to destroy this car (which is also trying to get away, so it might be safer to use a machine gun instead of the RPG for this one). It took about 10 seconds for me to destroy it with a machine gun.

If you are going to use 3 RPGs during this mission you still have 8 to use elsewhere, one each for Candy and Shell Shock and one (let's say 3 for safety) for Slink. So even conservatively you still have 3 left from the 11 you get during Riding Shotgun to use elsewhere (Ram Raider maybe). The mission Bishop (where you get more RPG ammo) seems to spawn only after this group of missions is done, but I'm not entirely sure. Either way, if you're careful with the RPGs (as in firing only on easy or important targets) they should be pretty useful.