He was on the way with Cleveland until the rug was pulled from under him.
That's speculation, and it's based upon only one season (1994), which then took a nosedive the following year (a nosedive that many blame on the team's ownership):
But was it really all about the move, or was there more to it? I generally give BB the credit of the improved 11-5 more than focusing on the following season, but.....
For example, Testaverde's numbers improved in several areas, yet stayed basically the same in key areas (i.e. TDs). And the team had moved on from Metcalf, and was no longer using Hoard in the passing game (A combined drop from 92 catches on 153 targets to just 13 catches on 16 targets), while the focus of that RB passing game became concentrated almost entirely in the hands of the aging Earnest Byner (from 11 catches on 15 targets to 61 catches on 84 targets) and a significant dropoff in yards per reception, as the offense fell from 11th to 25th, while the defense was dropping from 1st to 20th.
Looks like a couple of players did well while the rest of the team crapped itself, maybe over the moving situation, right? Well.... not so fast. Scoring (offense/defense)
1991: 293/298
1992: 272/275
1993: 304/307
1994: 340/204
1995: 289/356
Historically, his 1994 season is an outlier, both in his non-Brady coaching in general, and in his Cleveland days particularly.