Hello and Happy New Year 462ho,
Recently I had a Ford 9" rear axle made for my Chevrolet Caprice Classic convertible. I was like you initially and wanted to save money and find a used 3rd member with some sort of positraction.
I quickly came to the realization that trying to find an OE 31 spline nodular iron piece was out of the realm of possibility. Mainly because they are pretty rare and when you do find one they are outrageously expensive not to mention as DeepRoots said it would probably need rebuilding anyway.
If you're interested, here's what I learned when trying to piece a 3rd member together. First settle on your axle type (28 or 31 spline). The axle housing I had made came with 31 spline axles so I had to stick to that. Next pick out the differential type (limited slip, locker, etc) I found that the 31 spline axle differential more often than not requires a larger carrier bearing and by default a bigger bore in the 3rd member housing of which is next on picking out. Lastly choose the type of pinion carrier (std or Daytona).
Here's a quick list of how I pieced mine together you might find helpful, or not
* Differential - Eaton TrueTrac, I went with this because there are no clutch plates (uses spiral locking gears) and I came across a reference saying you will break your gears before you break the differential in the amount of torque it can handle. Another nice benefit is the harder you launch the more it locks both tyres together and conversely in normal driving it acts like an open diff. Plus no special additive, you can run regular diff oil. They offer this diff in 28 or 31 spline.
* 3rd member housing - Went with a Summit unit with the appropriate carrier bearing size (different bore options)
* To save a little money I used the pinion carrier and yoke from a spare galaxie 9" I have around.
For gears I didn't go as steep as you are planning, I ended up buying a 3.25:1 gear set as it's still better than the 2.73:1 gear set the factory 12 bolt still carries. I am also putting an overdrive transmission in as well.
If you like pictures here's a few.
Setting up the new gears.
To help save a few bucks I did use this pinion carrier and yoke from a spare galaxie 9".
This is the difference in carrier bearing for a 28 and 31 spline axle, of which you need the appropriate 3rd member housing to match.
Eaton TrueTrac differential.
The entire assembly.
Good luck on building your 3rd member!