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That helps.
To restate what I see as the problem; you’re trying to use the same resource to plan work hours and also determine cost for total project availability, which are two different things.

I don’t think there’s a good answer since every approach I can think of has a pitfall such as overstating total project hours, and/or over allocating the resource which results in extended project duration when leveling. I think the solution will need to be some method of separating the two (within the same schedule), using one method to manage work and one to manage costs.

Have you looked at Cost resources? I’ve never used them, but you can use them at the project summary task level to create an overall project budget and they can be used at a task level for project costs. If I remember correctly, they appear to be easy to setup, but I’ve never used them over the course of a real project to understand how they react or “report” actual costs as the project progresses.
If you can use the Cost resource to forecast availability cost, you may also need to set the actual resource cost down to Standard Rate of 0 so you don’t end up overstating project costs (availability cost + actual work costs). If it’s an enterprise resource, you can do this by changing the resource’s cost rate table on the task to use a table with 0 cost. Double click the resource name on the assignment and in the Assignment Information window, change the Cost Rate Table value at the bottom of the window. If it’s a local resource, simply set the Standard Rate column to 0.

Sorry I can’t give you a better answer than some ideas to experiment with. Maybe there’s someone else out there in MPUG land who’s used Cost resources and give some guidance.