Please take what I am about to say as one man's opinion with some experience. See comments below and in red in your quote.
Ok simple enough. I had to google a ladder frame because I have seen very few of them. This truck is definitely an X frame. By drop out I am assuming you mean third member that comes out? I was told non drop out Chevy axles take a special spreader tool to get the axles out and are expensive and a pain to work on. Is there any truth to that? NO.
I was trying to stay as original as possible but I cannot find the parts I need to connect to this torque tube axle. I thought 54 was open? The axle I found is the correct width and lug pattern which it why I liked it. The 6 bolt lug pattern is not easy to find. I am starting to think maybe I should go a couple inches narrower and plan on using a 5 to 6 lug adapter plate, which would put the wheels to their correct width. I assume you mean 6 lug TT truck is hard to find and you are thinking of going with a 5 lug car differential? The C10 axle looks like it may work with the original 54 brake parts that I already have purchased. Another fear I have is going with a much newer axle you will probably have different volume wheel cylinders. If I do that I will probably need a proportioning valve NO to balance front and back braking. Not a huge deal, just more time, money, and further away from originality.
If you have torque tube you need to wait for advice from AD folks as to what is involved with a different differential.
Yes, if by third member you mean it drops out the front, it's a drop out. If a drop out is the originality you want, use a drop out that' from TT.
Why are you needing a new differential? Can you salvage the old or re gear? I missed that part. Seems like you are doing what many have done. Buy an old truck made for hauling on yesterdays highways and want more speed.
There are probably GOBS of info in our search function regarding replacement diffs for 54. Lederman and others know this stuff.
I have found and swapped a few diffs in TF and have rebuilt a 1960 Dana 44. Not much AD knowledge except what I read. If I remember it all correctly.