This is what I (like to think) I would do.
You need to set them SMART targets, no?
Specific
Measurable
Achievable
Realistic
Timed
In the same email, state an overall timetable for results.
State also what you will do if the targets are not achieved. Then do that. As long as you are polite I think this is perfectly acceptable and professional.
Example: I would like a 2-page written progress report (Specific)to be in my inbox by close of play next Friday (Timed). It's Measurable because either you receive it or you don't, so there can be no quibbling whether it's been done or not; it's Achievable because they have the resources they need to do it (a PC and their expert knowledge); and it's Realistic because you're not saying you want it in five minutes' time.
Then say (depending on how arsey you want to be) something like, "please call me immediately if this is not achievable so that we can agree alternatives.
"If I do not receive this work by the agreed date I will be forced to subtract 5% from my next payment/actively recruit a new team of consultants/terminate the contract on grounds of non-performance." Though do check with your lawyers prior to this, or at least read the contract again.
Then, if they don't comply, or underperform, go through with your threat, or phone them up and say that's what they're going to do if you think there might be room for negotiation. You've given them fair warning; because your target was SMART you can prove they have not done what they should; in theory, they don't have a leg to stand on.
Any legal types want to chip in on this?