Whoever moves systems to the new provider before signing has given away their only leverage. Voluntarily, and usually without noticing.
I once witnessed exactly that. We were still waiting for formal approvals, but the running program could not wait. A fresh development system was urgently needed, and so the new provider „already got started“, although nothing was signed yet. Whether that would have saved us from the later escalation, I doubt, those were other, production problems. But it took flexibility and leverage away from us. For the provider, the case was settled.
What turns with the signature
With the signature, both sides switch from tender mode into project mode. With the provider especially, the air is then quickly out. As long as sales is in the game, it often has more direct and more powerful access to the decision-makers, and the closer to the signature, the more can still be pulled out. They do not want to let the fish off the hook. Once the signature is dry, a hopefully seasoned project team takes over, and some verbal promise from sales is then already history.
My advice to a board shortly before such a switch is therefore simple: have it looked at closely once more. Is everything really in that has to be in? Are the commitments understood as firm also bindingly agreed and not just soft targets? And does the shoe still pinch anywhere? Never sign out of exhaustion. Then rather pass the decision up a level.
Do not move a single system to the new provider before the contract stands. The leverage you have beforehand never comes back after the signature.