I'd personally rather fix the current carriage to, you know, keep everything original. And it should work. It's not like the escapement pawl is cracked or missing teeth where the whole typwriter depends on it.

Hoo boy!!  You got you a major one there!!  Looks like it's cracked all the way through, and if i'm not mistaken, that's cast iron.  The best way to get that fixed is to get it welded back together, and have you got a lot of parts to take off.  But if you do it step by step, and take pictures, you should be able to put things back together again.  The first thing you're going to have to do is to remove the carriage from the machine.  On an Underwood, this is fairly easy:  Remove the four bolts from the tabulator module in the back and remove the tabulator module.  Take the spring drum band off the hook on the left side (as the back of the typewriter is facing you) and place it on the hook-bolt on the main frame on the same side.  Be careful not to let it slip--otherwise you'll have to retighten the spring drum when you go to putting it back together.  Turn the typewriter around and remove the two bolts holding on the front carriage rail and remove that.  Then slide the carriage off the machine.  Now you have two more bolts to remove.  The carriage on this particular model is a two-piece since it looks like you have a basket-shift instead of a carriage shift.  There are two bolts on either side securing hooks holding onto eccentric adjustments at the front on either side of the platen.  Loosen these (do not loosen the bolts in the middle of the eccentrics) and open the 'jaws."  Now you can swing the platen section out of the way.  Remove the rack frame and take the lower piece of the carriage to a welder.  Installing everything back should be the reverse of what I wrote here.