Ahhhh, I love threads like this.
First off, I am a firearms enthusiast. I have made custom rifle stocks from scratch (wood, though), and have experience working at a firearms store installing aftermarket parts on rifles/shotguns.
The first dilemma I see with your plans, is the thought of just tossing a bunch of parts together, and ending up with a halo-looking firearm. Sadly, that's not going to happen . While there is a large variety of aftermarket support for pretty much all shotguns on the market, nothing looks even remotely halo related.
Now for my next point of discouragement... the coolest, and probably most unique, aspect of the m45d is the fact that the barrel is underneath, and the magazine up top. Simply bolting on parts will definitely not achieve this, and there are no available weapons like that on the market. In theory, you could literally flip the action of a shotgun upside down (if you don't know what I'm referring to as the "action" , please stop reading) . Hold on a sec, now the trigger is on the top of the gun, and the shells are ejecting right into your left forearm. Better start with a left handed shotgun... that will solve our ejection issues, but add some more $$$ to the project. Lets address the trigger being on top now. The only way you can redesign this, is with a fully custom receiver, and a custom trigger group as well, not to mention custom housing around the barrel for the custom pump arm and guides to follow ... we are talking $$$$$$$ for all of the design time, machining time, and materials.
If you are still adamant about having a functional m45d lookalike, I would suggest reading a heck of a lot more about firearms modification (your original post suggests you have a basic grasp, but still more to learn), learning a fair amount about metalworking (specifically aluminum), and maybe toss in some computer design learning as well. With these skills, you will at least be able to manufacture your own "body kit" for an already functional firearm, and do so safely.
Edit. Just checked out the ithaca m37.... definitely not a good starting point for this sort of project. It appears to be a very hunting oriented weapon, with no tactical style models or support. A remington 870, or similar, will have far better support for tacticool attachments and parts.