A useful information dashboard shows whether your project is on-track or at-risk. There is no single formula for determining that, especially when a project has fallen prey to the "80% of stuff is 50% done" anti-pattern.
Define Your Metrics
The problem with "health checks" is that they must be intrinsically meaningful to both your project and your organization. When you say:
Engineering had 40 hrs and $1600 allotted...they have used used up 30 hours and are only 50% complete[.]
there's no obvious context or action item. For example, is the point to say that you have to do the remaining 50% of the work in 10 man-hours, or that you only have $400 left in the budget? Is 50% the amount of value you've received from work on the current feature, or the level of effort remaining to complete it?
As you can see, there are too many ways to interpret this data. It may also be the wrong data anyway, because...
Fixed Budgets Aren't Level-of-Effort Estimates
Your question does not define how these schedules and budgets are arrived at. Are they based on fixed labor costs, or are they based on level-of-effort estimates for a particular milestone?
Based on the limited information provided in your question, the only valid conclusion one can draw from the data is that your current estimates are off by 25-50%. If this is a routine shortfall, then to my way of thinking you have a fundamental problem with your estimating or budgeting processes.
This may be a real problem (e.g. your delivery dates are slipping) or it may simply be a transient issue (e.g. schedule or budget will be made up somewhere else). Nevertheless, the point is that the project is not meeting someone's expectations, and that information should be disseminated and the process re-evaluated in light of your empirical results.