The only thing you need to change on a typical 2-stroke to make it run fine backwards is the crankshaft. It's the intake port cut in the crankshaft that "knows" forwards from backwards, everything else can go either way. You used to be able to buy replacement cranks, and maybe you still can, though I haven't looked for any.

As for moving the exhaust ports around, that's also possible. There used to be some engines (the old OS .40FSR was like this, I have a couple), where the front housing screwed on instead of being a one-part crankcase. This allowed you to take the front housing and backplate off the engine and swap them around, making the exhaust come out the other side. It was also possible to flip the carb 180 on it's mounts to move the throttle linkage to the other side of the engine as well (with or without changing the exhaust). So, with just a crankshaft, and some quick work with the hex drivers, you could have two totally mirror image engines.

As I understand it, the reason the brits wanted the p-38 engiens to both turn in the same direction was for spare parts inventory. If both engines went the same way, then you had exactly the same engine on both sides. If you had two planes, each with a dead left engine, you could pull one engine and put it on the right side of one plane and have a servicable fighter. With counter-rotating engines, you couldn't do that. Since the brits would have to ship in spare parts past the U-boats and so on, getting spare parts count down was really important.