Take this snow and shovel it

Stupid groundhog. He predicts an early spring and what do we get? A massive winter storm that's left four dead, hundreds of thousands without power, and everyone else with a load of snow to shovel.

Actually, in our yard, the problem is not so much the actual shoveling as figuring out where to put the snow. For people with normal yards, this process goes something like this:

1. Scoop up snow in shovel.
2. Toss snow to one side.
3. Repeat until paved areas are cleared.

Our yard, however, is not normal. In fact, if you were trying to design a yard for maximum inefficiency of snow removal, you could hardly do better than ours. The sidewalk is fairly unobstructed now that we've cleared out the hedge, but the driveway and the front walk/steps are surrounded by walls and/or overgrown shrubbery. So for us, the shoveling process is more like this:

1. Scoop up snow in shovel.
2. Lift shovelful of snow to waist height.
3. Carry it over to the wall.
4. Dump snow over the wall.
5. Return to snowy area and repeat.

Fortunately, we have only one car parked in what is technically a two-car driveway (it is possible to park two cars in it, but only if they're both small and have skillful drivers), so we can set aside a bit of area on either side for snow. Piling it up against the wall, however, isn't that much easier than dumping it over; every time you toss a shovelful of snow onto the growing pile, some of it rolls down the slope and back into the area you've already cleared. So it takes multiple passes to clear the pavement.

Every time there's a big snowfall, I curse the layout of our yard and rack my brains trying to think of ways to fix it. Unfortunately, I can't think of anything that would help short of tearing out everything, filling it up properly with dirt so that it's level, and then adding a completely new driveway and replanting. I know that getting rid of our overgrown foundation shrubs would help a little—at least I wouldn't have to try and crawl under that massive evergreen you can see at the far right of the photo—but the main obstruction is that wall, and I can't see any way to get rid of it. Maybe we could at least make it a little bit lower; in most places, it's well above the level of the dirt in the yard. That might help a bit, but I'm not sure how much, and I'm also not sure whether it could be done without knocking down the whole wall and replacing it.

So I'm left with two questions. First, the practical one: is it possible to remove just one row of cinderblocks from the top of a cinderblock wall like this one, while leaving the rest of the structure intact? And second, the more theoretical one: just how much trouble and expense is it worth to fix a problem that only crops up a few times a year? (Of course, as the globe keeps warming, big storms like these are likely to become more frequent, but it's impossible to predict how much will change and how soon. If I knew that, it might make the question easier to answer.)