Your plan sounds pretty good. The gravel layer is important. Use some landscape fabric on top of the gravel and perlite layers to keep fines from sifting down into the gravel/perlite. If fines gradually sift into the gravel, the floor can become unstable and crack, etc. also the pore space in the gravel is important for moisture control (capillary break).
Instead of gravel and perlite, I used 1/2" screened pumice (14" at the perimeter, 9" in the middle)(no expansive soils). If pumice is available, you might want to consider it instead of perlite. I think it probably provides a more stable base.
My guess is removing another foot of soil probably wouldn't accomplish much. Normally expansive soils that are problems are fairly thick. Dig a hole and see what the soils look like.
Sometimes you can get decent information from the
USDA NRCS Web Soil Survey too.