your question is very ambitous and komplex, because it's a great challenge to implement LED projects in rural communities.The reports, that I know, emphasise, that LED projects are mainly realised in urban areas, but can be realised in rural areas too.This indicates the great difficulties of your question, and it's clear to me, that rural LED projects are needed urgently in order to alleviate poverty. In addition I don't know your knowledge base and the background of your question (e.g.: Is it for a scientific paper or for practical use?).
For your insight, I added the links and files below. So ILO and world bank have an own website with the topic "LED". There you can perhaps find case studies or best practice examples of successful LED projects. In my opinion the trainer's guide manual is valuable (see below). There you find a "five stage sequence of the LED strategic planning process" (page 1), respectively:
Local Economic Development - The Five Stages of Strategic Planning
Stage 1: Organizing the Effort
Stage 2: Local Economy Assessment
Stage 3: Strategy Making
Stage 4: Strategy Implementation
Stage 5: Strategy Review
So relating to your question of best management models you need at any rate an integrative model like the New St. Gallen Management Model (see below). Such a model integrates different levels (individual micro-, institutional meso- and social macro-level), that you have to consider. In addition you can include the necessary change management or project management modells. Finally you can comprise normative, strategic and operative business management models, because you need them, in order to implement rural LED projects successfully.
I assume, if using such an integrative modell, you will already discover in stage 2 (Local Economy Assessment) differences between urban and rural areas. These differences could be valuable, in order to explain the difficulties with rural LED projects. I expect, you will find worse infrastructural conditions, more traditional values and life-forms as well as more fears of change in rural areas, compared to urban areas. If this hypothesis could be proved, you'll be able to deduce appropriate management models.
Many of the assumptions in LEDs are false or weak. One of the most glaring and one which is constantly repeated is the thinking that communities are homogeneous. The second is that every community has a product to offer tourism. It does not! Tourism is big business. To play in that game business models must be carefully crafted and tested.