Weren't they all contracted up to the end of an 8th season too?
No. Originally, they were contracted for six seasons. When the decision was made on a 7th, long and protracted (with Stewart and Spiner) negotiations began for ONE extra season.
Oh, and to the Berman-Basher (yawn): as some one else said, it was Stewart and Spiner's increasingly outlandish demands that nailed the coffin shut on the film series.
To the question: It could have gone one of two ways. If the option was to keep the same cast and same format as the last 7 years, then I think they definitely ended it at the right time.
However, if they were going to be a bit more daring (by choice or out of necessity -e.g. Stewart and Spiner were quite clear they would not do any more) and shake things up, then maybe it could've worked.
I always liked the idea of a season-long arc for TNG Season 8 in which the Enterprise is thrown out into the Delta Quadrant (what the heck - if TNG had continued, there would've been no Voyager, so why not use the stories?).
At the start of the season, have Riker promoted and Picard and Data off doing other things. Get a new XO and a new science officer - some variation of character we haven't seen yet.
I think the only way TNG could've successfully continued was to have shaken things up a bit. I was bored by Season 7, and so were the cast and writers - you can tell.