Projects always cost more than they are worth unless you get the gun for free or close to it, get the parts for free or close to it, and can do the work yourself.
Buy a barrel (if you can find one) for $125, pay a smith $125 to install it and refinish it at $300 with shipping and you have somewhere around $550 invested in a refinished gun with replacement parts. Now add whatever you paid for it to the total. Say you paid $300. That makes total cost $850.
Is a refinished 2nd Model 44 with replaced parts worth $850? That's for you to decide. It's your gun and your money.
It took me about 20 years of fooling with project guns to finally realize the financial folly of the notion. Better off to buy what you want in the first place.
But like I said, it's your gun and your money.