The flat strap bracing can be approximated as a concentric braced frame to get you in the ballpark for the upper structure drifts and periods. At 9 stories they may be hard pressed to get the end connections to work at the lower levels for flat straps and might end up with actual steel frames.

My Personal Open Source Structural Applications:
https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:
https://github.com/open-struct-engineer

Such is the double edged sword of delegated design. You can do a preliminary analysis and get a ballpark for the stiffness and then set a limit for the SSE to ensure the overall design remains valid - but if, for some reason, they find they cannot meet that stiffness requirement and the building is thrown back to a one-stage analysis your firm could be on the hook for the difference in price in construction - ouch. For projects of that size, a contractor is often on board early - even if it's not design build - to provide destructibility reviews and cost estimating. If so, they may be able to get you in touch with their SSE and you guys can work together - a novel and outlandish concept, I know.

Otherwise, you can either leave well enough alone and do the single stage analysis and the owner has to pay for 25% more building but your life is easier or you can you can go back to your client/the owner and say "for $X,XXX now, we can do a little more work and save you as much as $X,XXX,XXX later."

Some questions for you:

1) Is the concrete structure lateral system walls or moment frames? If it's walls, how long on average?

2) On average, how long will your CFM walls be?

I love the two stage business and use it often on 2+4 story wood buildings. It produces economical results and is often more reflective of true behavior in my opinion.

Unfortunately, it's pretty difficult to get super accurate with this kind of thing even if you are not doing the delegated design stuff. In my opinion, however, high levels of accuracy are not required. Seismic is always rough stuff so I support the telling of a reasonable story and the strategic acceptance of a little risk.

Consider some of the tricky things that would have to go into an accurate assessment of relative periods etc:

1) Accounting for all of the non-lateral CFM walls.

2) Determining whether or not your concrete shear walls rock at their bases.

3) The gobs of approximation that go into long term concrete stiffness and deformation estimates.

4) Accounting for the fact that much of your CFM structure period estimate work will depend heavily on the shear wall base connections which will suffer from elongation, slip, and even meaningful vertical deformation of the transferring concrete structure in many cases.

5) Soil-structure interaction at your foundations.

I'd make reasonable estimates of the things that matter and then, if a rigid base model makes sense to you, let loose the dogs of war / strategic business risk. Successful, free market, private sector structural engineering practice requires some -- not insignificant -- boldness. Put it to work for you and yours.