I'm not entirely sure I understand the question, so please forgive me if my answer is tangential. That said, I would ask the questions in the opposite order.
First question is (for me) always, "What does done look like?" Sounds to me like the first phase of your project is to complete a literature survey/market survey/research effort. Based on your comment, it seems like "Done" is "Determine the best architecture"
Personally I'd construct the decision matrix and preliminary weighting first, and then use it to direct my research. When the next unit of research won't change the outcome of the decision matrix, research is done. When I last did literature review, I could estimate the time fairly accurately based on the amount of published research; doing the decision matrix first would allow me to report complete in less time than that estimate.
At that point the relevant metric/KPI is the amount of uncertainty reduced by each time period of research. Technically you're tracking risk/opportunity - the reduction in uncertainty. Research reduces epistemological uncertainty; assuming that you start with the higher weight factors, eventually the epistemological uncertainty is small enough that it won't affect your decision.
I like crunchy data, so I'd probably model the decision matrix with a component that measures the probability of finding new valuable papers, but I'm a frustrated quant. Although I'd find it fun, I think it is actually overegging the pudding.
Some notes while I organize my thoughts: what follows will be under revision
There are a couple of tools that fit within the "decision matrix" grouping (there are others, and I'll add them as they occur to me, but the point is that there are multiple tools.
Analytical Hierarchy Process (AHP), which is fairly heavyweight, but may help if the factors affecting the decision are unclear. On the other hand, it is a front ended process; I'm not sure I'd want to revise the weighting if research were to change my understanding of the problem.
Decision Tree is the tool that was in every PMI course I took. Seems to be PMI's preferred tool. Probably not my preferred tool for this problem, since half the effort seems to be setting up the tool, and doing so implies to me that you have a deeper understanding of the problem than is appropriate for a research scenario.
Decision matrix - this is closer to what I've typically used. Unfortunately this is why I need to take time to organize my thoughts. Reading this page makes a relatively straightforward process seem like rocket science/PhD material. I need to find a way to simplify this to the actual process.
Fundamentally, all of these tools reduce the problem into a choice, and a set of factors that affect that choice. Creating a trivial example, if I have a set of software requirements (functional, and nonfunctional) {R}, and a choice of architecture A or B.
For each r in {R}, can it be expressed more simply in A or B? Are there examples in the literature of successful implementations? Are there known limitations?
Are there relevant resource constraints for A or B? (Do we have the relevant skills on staff? Does our intended hardware support? Will we need to provide any infrastructure/logistics support in order to market the software?) - NFR's such as performance, security and logistics may show up here.
I'm going to make the example really trivial here, but if the choice is between Architecture A and B, and the factors influencing the choice are R1, R2, R3 then we need to assign weights to the factors (R1 is 5 times as valuable as R3; R2 is half as valuable as R1). At the beginning of the search, A & 5 are each 50% likely. As we identify relevant papers, they will affect the weighting. If we find a set of papers that indicate that Architecture A has been used repeatedly to fulfill requirements like R1 & R3, then we apply the relevant weights to shift towards architecture A. On the other hand if there is zero evidence that Architecture A has ever been used to support R2, that will have a lesser, countervailing impact.
Returning to your fundamental question - how do I use this to bound my search? how do I measure progress towards "done"?
I still think the coarse measure, and the one I'd use for day to day, is a linear measure of exhaustion of my search space. Inelegant, but I'm willing to bet that it will be close enough. (It is early in the morning, and I can't think of a name for the class of metrics that are like yesterday's weather; embarrassingly simple, but good enough for practical purposes.)
I would also work from the assumption that I'm going to find the most valuable results early. I'd calculate the interval between finding useful results and plot the curve of days between interesting results - I'm willing to bet that curve will be a familiar long tail curve, and that I can use that to predict approximately how long it will take me to find the next interesting result. (it is 80% likely that it will take between 5 and 10 days to find the next interesting result).
I can look at the decision weight (Architecture B is leading 80% to 20%) and the predicted time to next interesting paper (80% likely to be up to 10 days), and estimate the probability that I will find one or more papers that will affect the weighting by over 16% is less than some threshold. And I can use that to terminate my literature search early.
