I think you need to specify whether the project is a speculative (profit-oriented) or social (public-oriented) one or both. The purpose of a project will more often than not inform the methodology used to evaluate or assess it.
It would be helpful if you give us details about your PhD. Nevertheless, bounded rationality seems a more realistic option in most of the scenarios where human beings are involved.
As projects are by definition unique, uncertain and complex tasks, rational choice assumptions are corrupted. Bounded rationality is the basis for real life project behaviour. If Your aim is to improve project decision making, bounded rationality is Your choice.
Project success, though, is measured in hindsight. In hindsight uncertainty is no longer a part of the picture and You need not take the uncertainties at the time of decision into consideration. If Your goal is to analyze how well the outcome actually happened to turn out, be it by luck or skills, then the analytic rigor of rational models may be preferable.
Economists are coming to grips with modelling boundedly rational decision making, at least partly, for instance by introducing cost of information with unknown value. There may be something of interest to you in that line of reasoning. It is commonly referred to as behavioral economics, inspired by Kahneman and Tversky's prospect theory.
Gerd Girgerenzer opposes the conclusions suggested by prospect theory, arguing that robust heuristics produce better decisions in complex and uncertain situations. Prospect theory is in vogue, but Girgerenzer presents the better argument. Still: In hindsight, sucess may well be analyzed in terms of rational optimalization logics.
Your own decision problem is one of 'project front end decision making', illustrative of the assumptions of bounded rationality. I hope Your Choice will turn out a lucky one ;)