Ranks go up exponentially so it slows down the higher you go. The trick is to keep doing missions, trading and turning in bounty vouchers, but also keep moving around - once you are allied with a faction, your superpower rank will stop going up even if you keep doing missions or whatever for that faction. So you need to go from system to system becoming allied with as many factions as you can.
Edit: or you can cheese missions for a few days and end up hating your life, that works too. But unless you know for a fact you're going to like that ship, I wouldn't do it. You'll want those days back and you can't have them.
If I'm understanding part of what you wrote correctly, well, you are not correct. I can assure you that being Allied with a faction does not stop you from getting Federation Rank from their missions.
To the OP:
There are a few places where this could be done quicker prior to 2.3, but I'm not sure if any of them are still valid. If you are looking to do this in the shortest amount of time, then you want to utilize locations that have data or delivery missions with short runs that preferably go back and forth from the same stations. This is somewhat mind-numbing, and will require mode-switching to get a full set of 20 missions at each stop, but there are a couple of upsides. First, you will become Allied with the Federation-aligned factions very quickly, and if you are able to take some of the cargo missions, your Trade Rank will also go up. Second, once you are Allied, and have a decent Trade Rank, this method of mission running pays very well indeed. So well, in fact, that you will likely earn more than what you need to purchase the ship before you can even buy it (assuming you can do at least one cargo mission that pays 200k+ each way). If you have a Python, you can take several of those missions each way. As a point of reference, I made over 150 million credits while doing the last two ranks for my Cutter. That was after roughly 40 million spent on Donation missions (do these if you can, instant mission completion)
Some locations to try:
Sothis/Ceos
Chakpa/Ochosi
Niu Hsing (might be spelled incorrectly, but it's close)
Barnard's Star (Haller City) - this one isn't to-and-fro, but you can seemingly grab an endless chain of Federation missions from each stop.
Remember, these were pre-2.3. They might all be broken now, or maybe the BGS just needs to spin up a bit before they get back to where they were.
Good luck, and keep your eye on the prize, if you are going to grind this out. I would suggest setting a number of loops (defined as 40 missions, 20 each way) per session that fits with your play schedule, and gives you progress that you consider to be meaningful, while leaving options open to break off and do other things.
If these are broken, and you want to try to find your own, then you need to look for at least two systems that are close together, but are also somewhat remote from anything else. If you find such a setup, they should have missions that primarily run to and from each other.
Edit: One last thing - make sure you buy your Corvette from a Li Yong-Rui system, as it will cost you a lot less. The modules, as well.
Second Edit: Chakpa is currently in lockdown status, so I wouldn't bother flying there just yet. Maybe the next state will be better.
Riôt