CS for a single tenant build-to-suit

The challenge in this situation is defining who has "control" of the project design and decision making, and thus what scope of the project is included in the "LEED work" getting certified. If a building owner was going to purchase and occupy the existing building and construct the new building for their own use, it would clearly be a NC project. If a building owner was doing the project as a speculative development, and didn't have control of the tenant improvements (TI)/ interior fit-out, it would be a clear case for using Core & Shell (CS). In practice, projects are rarely built only "on spec" and so some or all of the tenants have usually committed to lease agreements before the project starts. Still, the owner's core and shell scope of work is clearly separate from the interior fit-outs, so it's reasonable to certify just the core and shell work and systems using CS. Appendix 2, 3 and 4 of the BD&C Reference Guide are used to define the scope of work getting certified.
With a "build-to-suit" development, it can be less clear, since the building owner is undertaking the project for this one particular tenant, and thus both parties are negotiating what will and won't be included in the project. We've seen cases where this went either way – NC or CS – and largely depends on whether the tenant "wants" their interior improvements to be certified.

If they don't want their TI certified then you could pursue CS as you propose, but you'd need to clearly separate the design and construction work of the core and shell and the TI for LEED documentation. Easier to do on the design side if you have different design teams, as you do, but harder for the single construction manager who is doing both parts of the work: they would need to separately track all the materials costs, VOC compliance, recycled content, distance of manufacture, construction waste, etc. for just the core and shell work scope. In some cases it might be hard to exclude the materials or effort for the TI work, especially with construction waste, or work like ceiling grid that might be done for both core and tenant spaces in one pass. It's certainly possible to get all subs to do separate bids for any materials and work that will be done in both core and tenant spaces if you plan for this ahead of time. Keeping the waste separate will be harder.

If the tenant wants their space to be certified, and know that their interior work is being done to meet LEED requirements for VOCs, etc, you can certainly combine both core & shell and interior work scopes into one LEED NC submission. Easier on the construction management side, but more complicated for the design teams, who will need to collaborate on some of the letter templates for mechanical, electrical and plumbing (MEP) systems.