Romeo, this is a thread I have been thinking about starting and you just beat me to the punch.  Like you I would like to have a 44-77 but unlike you I am considering putting one on a rolling block I have.  I have been doing some research and have seemed to find the most information over on the Shiloh Rifle Forum. There are a hand full of shooters on there that enjoy this caliber as well as some of its siblings, the 44-90, the 44-70 and several of the 44 straights. 
Greenmountain makes a 17 twist .44 barrel but to my dissapointment they do not offer it in the Winchester #4 weight, which I think would be about the proper size for my roller. However in your case, a round blank may be what you would prefer. 
BACO (Buffalow Arms Co) offers several off the shelf molds for this; caliber and Jamison is now selling proper stamped, brand new manufactured brass. 
The things that I have not seen, or have missed over on that board is who makes the best, proper reamer for this caliber, as well as what is the best lead to have put in the throat. I have seen both 11 and 7 degree leads mentioned but no one seems to say what is best. I do know that if you plan on using paper patched bullets, you will want some lead into the rifling as opposed to just the standard reamer will put in. 
Hopefully there are one or more shooters that enjoy the 44-77 on here that will jump in and help both of us out.
Sam

If I remember right Kelley Roos who posts on the Shiloh forum and others, has a 44-77 built on a hiwall. I'm sure he can offer suggestions.

The bore/grove dimensions for the Green mountain barrels are .438/.446 with a 17" twist. If you would like a different make barrel, go to Buffaloarms.com, they carry badger, Douglas and kreiger barrels and blanks. 
I don't know why, but at one point Green mountain offered a #4 weight barrel in .44 but now you can only get a #3, #3.5, and a #5. 
Personally I would like to have a #4 to put on my roller but in all probability will end up using the #3.5. 
The 17" twist should allow you to shoot well up into the mid to upper 500gr. weight range wthout any problems and should stabilize that weight out to 800 to 1000 yards.
I hope you keep us informed on the progress of your project and how well it shoots when its finished.
Sam

I would like to correct myself on what I said in the previous post. A 1-17" twist .44 should be fine. There was a fellow at Lodi this fall that had trouble with the 44 but I believe he was shooting a 1-19" twist.  There is some talk here of trying 1-16" but so far I think it's just talk.  I'm sorry for the earlier post.  Bob
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Bob, the good folks at Shiloh use a 1-19 twist on their '74 Sharps rifles and from what I gather from reading the Shiloh boards they do shoot well.  Yes there is some talk on there about using a 1-16 twist on the .44's but I think, that those people are looking at 800 to 1000 yard use for the 44-77 and others of that family.
IMHO, the best thing to do is figure what ranges and uses you are going to be involved with, then pick the bullet weights you plan to use, do the math with the greenhill formula and get a barrel with the proper twist.
If 1000 yard work is your goal with a very long heavy bullet then by all means look for a faster twist. If shorter ranges and lighter bullets then a little slower twist will most likely get the job done.
For me personally, I think that a GM with a 17 twist will do everything I want it to do.  For Silly-wets with a 500 gr postel bullet, that twist should be more than enough and should still hold out to 1000 yds should I ever want to give that game a try. For hunting, a 400 gr. flat point should still shoot very well out to 200yds or so. 
In doing the research on the 44-77, I have come to 2 conclusions, the first being that it can be a lot of work and frustrating to get things just in the right combination to shoot well.  The second being that once you hit that majic point, and everything comes together,  you will have something that will work beyond your expectations.
These are just my opinions, your mileage may vary, but its my story and I am sticking to it.
Sam