The current idea is to make a very detailed plan for half of the available funding and reserve the half to make 4 very specific customizations to the project for each client. Obviously the exact needs could be researched much more deeply as well, to split the funds 60%/40% etc.
You're allocating the funds in an appropriate manner, splitting the initial cost for both clients at 50/50 and splitting the remaining customizations at 50/50. This is a great place to start negotiations. Depending on requirements overlap, this may change.
From WikiBooks PMBOK Scope Management:
Scope refers to a project’s boundaries: it determines what work will be completed during the project lifecycle. This includes identifying the work that won’t be included in the current round of product/service development.
If you're going to ask two of your clients to split the cost of a portion of the project, you're going to need to know exactly what requirements both will agree on and exactly what requirements will be paid for and worked on separately. You must clearly define those scope boundaries; disagreements in agreed-upon requirements, changing requirements, and scope creep that heads in completely different directions is a huge risk to the combined projects.
As you're aware, your job in managing scope is going to be a lot tougher than if you're dealing with only a single client.
First, you need to make it clear to both clients that the items that they agree to split cannot be changed without revisiting the entire scope.
If, theoretically, 50% of the work is split for the same requirements and 50% of the work is directed towards differing requirements, and client A decides to change a requirement from the shared category, then does that mean that Client B then picks up the costs of the abandoned requirement, or do you hold Client A to that cost?
You'll need to get an agreement up front as to how to handle these scope changes to determine who pays for them. Despite the clients being used to getting what they want, you'll need to clearly define the scope and hold them to that. In the Project Charter, pay special attention to details such as Project Manager authority in changing the scope and clearly define the budget for both sets of requirements.
Communication and negotiation skills are a “must-have” as well. Project managers need to educate stakeholders about the project impacts of some requirements. Adding complexity to a project may require more staff, time, and/or money. It may also have an impact on project quality. Some aspects of the project may be unfeasible – stakeholders need to know this so they can adjust their vision or prepare for future challenges.
Moreover, you may discuss with the clients to gauge their tolerance for cutting features, if necessary. If Client A absolutely requires that you expose an API to allow them to integrate one of their databases, and they're not willing to pay more, then come up with a plan for what features are lowest priority from the non-shared 50% category to make up for the differences in time or cost.
Ultimately, it's up to you to ensure that the scope is realistic and that you can meet the needs of each client, and this will involve some negotiating on your part as well as drawing from your past experiences as to what is and isn't doable.
Lastly, if these clients are known for changing requirements or pushing for changes that add scope creep, you may want to consider both of these as separate projects. The costs will be higher for both of the the clients, and some work may be duplicated, but it may be easier to guarantee that both clients get exactly what they want as the risks will be lessened and more transparent.