Imposing an arbitery maximum is not going to work as there is such a large standard deviation between estimations at each point/tshirt size. That SD is the very reason that we use relative effort estimation instead of making up a number of hours that will be wrong anyway.
Now if you are working with third parties, or contractor's then you need to think in sprints. If you have a fixed length sprint, and fixed number of people then you have a fixed cost for you Sprint.
The thing that then varies is the velocity, or the amount of delivered functionality, in each Sprint, or done increment.
I guess you might know your budget going in, and you can decide the budget by the sprint cost and see how many sprints that you can fund.
You set the team to delivering at a sustainable pace and each sprint you have working software. You can stop at any time, and you can ship once you are happy.
If you are unhappy with the velocity then you need to deal with that. You could add more teams, make the team bigger, or stop development.