Technically speaking, inserting at an angle shouldn’t violate the rules. The trouble you’ll have is getting the right angle. You’d just be guessing. Plus to get the right angle to get the correct steer, you couldn’t just insert it into the slot, you’d have to find a way to angle it in a little too. I wouldn’t recommend as most likely you’ll make yourself slower rather than faster.
While shaving the body does seem illegal, it can be within rules. Most likely your rules state your car must be 1 3/4 inches wide says nothing about shaving the body. If you shave 1/32 from one side and add 1/32 to the other side, it’s stikl the same width and within rules. I did this for our tech day and it worked well. Our car was noticeably faster than the other cars, but it has to be a rail rider to make a difference.