I know I'm way late here but in case this helps others -- yes, it's a definitely flaw of this game that they fixed in the sequels.
I find that if you join the special campaign organizations as soon as the game allows you, you can end the game in ~10 years of the game time. But that means that even starting a campaign in Late era, you won't even have access to some of the end-era ships that come out between 2290-2300 (like the Heavy Battlecruisers).
The most fun I've had to work around this is to play out my share of the standard missions, gaining points and buying as many legendary officers as possible, and getting the best smaller ship for the time (War Destroyer Leader, Command War Destroyer, Command Light Cruiser, etc.). Then join the special organization and have fun and let the game take you to its end.
I tried recently to flub mission 8 or 9 so that I'd be kicked out of the special group and could play endlessly, but I think after a certain point, they won't kick you out.