On astock NA elise I run R888r stock sizes, 195 up front and I think the rears are 225.
As others here have said if youre runnign 888's for track they should be 888'r, otherwise whats the point.
At a recent autocross my NA elise was the fastest of the loti there except for someone running yoko slicks in a 211. Even then the time difference was only 1/2 sec.
In an autocross I never felt any lack of rear grip, if anything there was understeer, had the same issue running yoko slicks on a full track, and there the fronts were 205. The reason is simple, I'm running a stock street trackpack setup on this car. More negative front camber would cure any understeer. Wider tires are not the way to go, they will just mask steering feedback and you run the risk of rubbing. Lotus actualy knew what they were doing when they came up with the tire sizes.
As others have advised, adjust the aligment first before you need think of changing tire sizes, and def get the R's if youre goinnto the track.
As an example of camber, on my exige v6 track car we started at -1.9 front and it understered, now at -2.4 same tires its the rear that cant cope. Yes lots of negative camber affects street driving in that the car wants to turn in more, and if youre not on track the inside of the tire will wear quicker than desired. But somwhere there is a happy medium, and I would start witht he 195 up front first and find the balance of the car.
What are your current camber and toe settings?