Converting your measurements into inches and then figuring out the volume, it looks like your tank would be 125 gallons (correct me if I am wrong). Typically with cichlids, you want to overpack a little (but not go crazy) to minimize aggression. Some people use this as an excuse to put a billion more fish in their tank than they should. It really just means to go a little above the limit. Keep in mind that with this overpacking comes the added responsibility of increasing the filtration. More fish in a smaller volume means need to buy more filtration than is typical for a 125.
So most mbuna cichlids reach 5-6" in length as mature adults (so let's just say 5.5 inches for the calculations we are about to do). There are of course variations, but this is the average. Haps and peacocks can get bigger so you would need to adjust for this if you plan on keeping them instead of mbunas. 90% of the people who say cichlid mean mbunas so that is usually what I assume. I know the "1 inch per gallon" rule is way too generalistic and not accurate unless you have smaller fish, but it will work to give us a ball park for your tank. So, using this rule, you would be able to keep 125 inches of fish. Now, to overpack, I would probably go up to 140 inches to 155 inches or so. This means you are looking at 25 to 28 adults in your tank.
You are right that many mbunas reproduce like crazy and you will soon be overrun with fry. You can do several different things here. You could limit the number you originally buy and then let the fry grow up in your tank. You could separate the fry into their own tank or you could just sell / give them to people or local fish stores as they are born. I do the third option. I let the fry get around 1" or so and then I sell or give them to local fish stores. I also trade them or give them to people here in town such as dizzcat.
The main thing to remember, and I can't stress this enough, is to get filtration setup on the thing like it is a 175-200 gallon aquarium. Cichlids are messy and you will be overloading the aquarium. They must have the filtration to match if you want them to be happy and healthy. And of course, as you say, you can't drop 25 fish in the tank at one time. You would build up to that number over time exactly like you said in your post.
Good luck and congrats on the new tank! Post some pictures when you get it up and running. I love looking at cichlid tanks and what people do with them.