Those bushes don't look like they need a truck... dig one and find out. Putting a truck on the lawn is going to do a lot of damage, not to mention the damage from ripping the bushes out of the ground... it also looks "bush league" doing it that way, tearing up the guys yard for a couple of bushes. Get a good "Pony Spade" at about & $85.00 It'll cut through the roots like a hot knife through butter. I'll bet the Diamond has one. I'm 57, I still dig, in the summer, in South Florida where I am familiar with heat.
You may want to use a service to make sure you don't have cable or pipe running under there before you start ripping and tearing. We have a free service down here called "no cuts' they scan the area and mark all the utilities, if they miss one it's covered if not and you break it it'll cost you.
The trees aren't that big, like the man said, cut a notch and then make a slow cut from the other side and you can do a "controlled" drop using the hinge. I don't think they'll do any damage other than scratch the asphalt a bit. Anyway, smaller branches will break the fall. Depends on how much sack you got and how much work you want to do. The quicker you get it down, the better.
$2,000 for those trees sounds like a lot for down here, but I'll bet you can get $400.00 - $600.00 each for them, including the stump grinding. If it's hard wood, you got some for the winter, so it's a bonus.