It's always hard to tell second-hand, but this has the odor of something slightly shifty. Most positions want the contract signed up front, before you even touch an asset, as it also protects their legal liability and outlines the terms of what YOUR limitations are (like NDAs, HR policies, etc)
I think if you've been trying to get the contract signed for a month or more, it's time to go to your boss's office and make him sign it. If he seriously doesn't have time to sit, read it, and sign off, then you may even want to mention your discomfort with the situation and that you don't like the instability of this being undone. This is really rather weird, as contract agreements are rarely modified, so it's pretty much boilerplate - if you've signed off on one before, it shouldn't be more than a quick look to handle it now. You may need to be gently pushy - bring the paperwork to him, offer to file it - basically eliminating any legwork beyond the boss signing his name.
Then when the paperwork is clean and clear, start addressing the pay differential as a mistake - maybe with accounting or HR first - ask them to explain the math and why your net payment is lower than you expected. It may be that you are out of the loop on something and they can explain it away. Check with other employees if you don't buy the explanation, and raise it to the boss if you don't get an explanation or if you disagree.
I just say push for the documentation to be signed before you start agitating on pay, because the two together sound incredibly sketchy. It could just be bad paperwork but it could be the company trying to dodge away from paying you what they offered, in which case, having the contract in writing will help you a great deal in having some leverage.