Shimming the Hop-up and Accuracy

Today I took my relatively new rifle out for a real range and accuracy test, and to get a feel for my new scope as well.

The gun fires pretty well, although I can't offer any really professional groupings because it's a stock rifle. I'm satisfied with its current range, but that can be buffed later when cash is more plentiful. It works nicely, until you add hop-up. I used a fair amount of it, but my accuracy went kaput. BBs were curving left and right like nobody's business, it was actually kind of silly. I immediately turned my hop-up completely off and the shots went back to the usual predictability.

Now, it's not necessary at the moment, but I had the feeling that I might be able to get a bit more reach by way of adding a pinch of hop-up, but as I explained that's simply not possible with how unreliable it makes my accuracy at range. After exhausting other easy avenues, such as cleaning the barrel and maybe the BBs, how should I go about shimming my hop-up arm? Would that fix my problem, or am I missing the underlying cause completely?