If you haven't seen it already, this page has some helpful, basic information about the AMC 20 compared to the Dana 44. It also has information about identifying the gear ratio:
Also, for what it 's worth, here's a post with 2 photos that show where the letter is stamped into the AMC 20 to identify the factory gear ratio:
To answer your original questions about what direction to go, it all depends on how much time, money, and effort you want to spend on the project. If you're more of a casual offroader, then you may want to get the AMC 20 crack fixed, get a better gear ratio in it, and be done with it and get back on the road. Note that if the housing cracked, then you might also need to consider replacing other parts as well (shafts, gears, seals, etc). If you want to go a step further, put in solid (1 piece) axle shafts to replace the factory 2 piece (shaft + hub) axles. You could also reinforce the AMC 20 as people above have mentioned. If you want to go all the way, find a totally new/different axle assembly and spend the time and money to get it installed and set up right.
A big part of the equation also involves how much of the work you would do yourself versus paying a mechanic to do it.
And also, welcome to Jeepforum! Glad to have you on board!