Welcome to the forum, you'll get lots of good help here AND opinions.
Pulling your engine in the bird is really simple. I've done alone many times. There is another post here somewhere about some different ways to do it.
An important safety note is in any case make sure your engine lift has adequate length legs on it to support the weight and angle at which you will be operating. This can go wrong in a split second.
Some go from the side. I go from the front, first removing the hood. which can also be removed by one person with a picker. And I always pull the tranny with it.
Because of the nature of most pickers, they don't quite want to reach into the engine bay far enough on tbirds, the 57 is worse because of the depth of the front bumper. You could remove it (An extra PIA) or like I suggested get extensions for the picker, or go from the side. (never used this method).
You can also have one of your friends (pick a weighty one) stand on the back end of the picker. (not a recommended method) but i have done it.
My vote is to get some exts. for the picker and be safe, not sorry.
On the trans you sound like you have it diagnosed, are you going to have it done or diy? Myself, I farm that work out.
BTW that trans is a pretty good one but heavy, there are ways to improve it as per the Hoosier hurricane. But it's your call. Depends on what hp you want to make with the 312? In most cases street use,etc. I would rebuild it and drive it.
A L A N F R A K E S ~ Tulsa, OK