TBH If you're not Inheritor by now then you just don't have the dedication to do it. ^__^My 360 broke back in 2011 so I never touched Reach again until it recently became backwards compatible with XB1. In 1 month of casual playing, I went from Recruit to Brigadier Grade 1. That's roughly 1.5m credits.
Just playing normally over the course of these past 5 years should be way more than enough to get you to inheritor.
I found Grifball to be the fastest credits by far. 9/10 times I get matched with players who prefer to just idle with the bomb and never score. I get about 8,000 credits per 15 minute game, which means a max of 32,000 credits per hour if I'm lucky although realistically its usually 15,000-25,000.
BTB is also decent, but not nearly as good. (Frequent teammate quitting and therefore: losing)
If you want to play solo, 2x Score Attack and Gruntpocalypse are the best gametypes in Firefight. It takes me 7-8 minutes to finish a game and I get 1500-2000 credits per game. 2x Score Attack is also great for getting your commendations up.
That's my boy :P
Grifball as I said, is a faster method but Firefight is safer.
Specific weapon "Attacks" give you an extra + 50% damage (= 150% ) and replace the Armor Lock with Evade, final waves aren't stealth Elites.
And I would say Skirmigeddon is faster and safer than Gruntpocalypse since Skirmishers run faster and aren't as dangerous as Grunts that can throw grenades and use Fuel Rod Guns (they can headshot you that's all) , I never noticed if Skirmisher kills give more Cr than Grunt kills but always aim for the head for headshot kill which is a commendation.
Since Skirmishers don't use explosive weapons, they can't kill themselves like that unlike Grunts or Brutes.
You can play normal Firefight with random players too, normal Firefight is like triple Score Attack (one set, not one round) , average reward is around 5000 but you have commendations kill (heavy, precision, automatics, vehicles, etc... ) that add even more Cr.
took around 1.5 years to reach Inheritor, some Grifball here, tons of Firefight games, some coop campaign games and a lot of custom challenges (the usual 1000 kills/medals in Firefight that give 20 000 Cr, yes two challenges at the same time) .