Speaking as an ex-manufacturer, this is the process I would recommend to maximize your benefit as an integrator:
1) Meet with the customer, multiple times if necessary, figure out as many of the basics as you can: needs/pain points, do they have budget (how much)?, when do they want to have this implemented, what will their purchase process be (bids on same system, multiple quotes from integrators, etc). Get yourself to the point that you have a pretty good grasp of the overall opportunity, including timeline, budget, and things that could potentially derail it. Document all your meetings along the way (dates/times, people present, topics discussed).
2) Tell the customer you have a few companies in mind that you think could meet their desires, and you would like to bring the right people from those companies in to discuss the project further.
3) Go to your manufacturer sales guy, lay out of the project. Make it clear that you have control of the customer/project (this should be easy, based on your involvement in step 1 above), tell them you'd like to bring them in to discuss solution, do demos, etc.
4) Work with manufacturer sales/pre-sales to come up with some at least rough design proposals. Does not have to be too involved at this point, just something showing joint work/effort.
5) Schedule meeting with the customer/yourself/manufacturer. Introduce manufacturer sales person, let them lead majority of the meeting, demo/sell their product, etc. Go over your design proposals or general approach to solving their problem. Followup afterwards (next day), ask customer for feedback on what they thought of the presentation, etc. Give that feedback to the manufacturer from the meeting and/or use it to refine next presentation, or select alternative product.
This is simplified, and it is not always quite as easy as I have laid out, but in order to make your value and involvement clear, you want it to be obvious that you are in control of the overall process, and have the contacts and "pull" with the manufacturers to get meetings scheduled with them. If you jump right to bringing the manufacturer to your first meeting you have a greater risk of being marginalized, as the manufacturer is more likely to monopolize the meeting, and thereby the overall information flow and control of the deal.
If you are using manufacturers reps, invite them in step 5, but in addition to, not in place of, the actual sales rep from the manufacturer. On a go-forward basis, you may be able to have just the rep in future meetings, depending on what is being discussed.
I would minimize involvement of anyone besides people from your company at the initial discovery-phase meetings. Build a relationship with the customer, as much as possible, before bringing others into the deal.
Also, following this process should set you up for any registration discounts or similar protections the manufacturer offers, which helps you, at least to some degree, if it ends up with multiple integrators being involved, through whatever mechanisms.