The simulation facilitator who is guiding the simulation and running the debrief should be trained in sim facilitation and theory-based debriefing.  Using the INACSL standards as a guide, the “sim specialist” should not be doing everything. Whoever is conducting the theory-based debriefing will need to be focused on watching the simulation scenario play out to capture the learning moments, etc. A faculty member can participate in any aspect of the simulation, training is necessary so they can fully engage.

Direct your faculty to the INACSL standard on Debriefing.  This standard guides how the simulation component of Debriefing is managed. I would start here and engage your colleagues in a conversation on a theory-based method they can all agree on and then decide for faculty development in this area. Here is the link to the debriefing standard:

http://www.nursingsimulation.org/article/S1876-1399(16)30129-3/fulltext

 Key faculty in courses can be trained to engage as content experts during the debriefing and the trained simulation facilitator can manage the overall theory-based debriefing with students. This means that the simulation lead guides the debriefing and directs specific questions to the faculty/clinical content expert. Standardized patients can be played by faculty members.  Work-study students can be trained to operate the simulators and stage and tear-down scenario settings.  These are some of the work arounds being used when funding is limited. 
The most important consideration is the curriculum planning.  If staffing is an issue, begin there and determine the necessary resources and staffing requirements to run one simulation. Determine how many faculty course loads can then be allocated to simulation activities beyond that. Once you know that, then you can determine how many hours of simulation you can work with. Review your curriculum map and determine where simulation is essential.  An important consideration is to identify those patient care situations for which every student should have an encounter.  If you can only run one simulation per course or semester, then you start there. Good teaching takes planning and sometimes, thoughtful work arounds. The important consideration is what will be the learning outcome for the student.