I think in order for SEGA to become what it was, it would need to be bought out by an understanding American or European company.
Take out all of the management. Keep the employees and just tell them to get their creative caps on. Market their products depending on how well you think they will do (if a game flops, give them a smaller project, and vice versa if a game does better than expected).
Branch out your teams to look into other areas (for instance, perhaps AM2 makes the Arcade games, help them look into ideas on how to get their games onto consoles/handhelds without causing too much risk to their original vision of it being an arcade game...perhaps cut some content for the consoles, but give them an incentive as to why the Arcade experience is better!).
Give Sonic Team a rest from Sonic (unless they have a good, non-gimmick idea) and let an American company do something with Sonic without disruption from Sonic Team (but of course, I wouldn't want them changing the genre on Sonic either). I'd give Sonic Team two projects on handheld and console (nothing too big a budget), and advertise it well.
From what I currently see, SEGA has always been good at B-Tiered games (nothing wrong with that! It just means the games are of a reasonable price and usually have innovative ideas), so I'd market SEGA games at a lower price of $45/50 - £25 to entice anyone on the fence.
The company should also make sure to convince retailers to keep their games on the shelves too and advertise to potential gamers as to why the new game is worth their money.
Some of you may disagree with me on this (and it's fine), but I do like some of Nintendo's own marketing ideas like Iwata Asks and Nintendo Direct, even if it just targets a certain audience.
I'd advertise games like Sonic/NiGHTS and the like on Kid's Programs and at Prime Time, so the exposure is maximized and hire some influential artists to make the cover art stand out on shelves (something SEGA did a good job back in the early 90s.
Just some of my ideas.