Hi Mark,
I agree, it can get quite confusing. Hopefully I can explain it clearly.
There are basically three types of K60 parts:
100MHz 1.x parts - on TWR-K60N512 board - no SPI1_IN on PTE1
100MHz 2.x parts - on TWR-K60D100M board - has SPI1_IN on PTE1
120/150MHz parts - on TWR-K60F120M board - has SPI1_IN on PTE1
The differences between the 1.x and 2.x 100MHz parts are in this app note and it includes the change in SPI1_IN that you noticed. Likewise a K60 device going from 100Mhz to 120MHz has differences as well described in this app note (it specifically talks about differences between Kinetis 100Mhz 1.x to Kinetis 120MHz, but you'll notice a lot of the differences described are still valid when going from Kinetis 100Mhz 2.x to Kinetis 120Mhz to cover changes required for new modules on the 120Mhz parts). So while they are all generically a "K60" part, there's quite a lot of internal differences as you see. Also yes, the K60F 150MHz reference manual is valid for the 120MHz parts (there's a list of parts a particular RM is valid for on the first page).
That all said, the external pins were meant to be compatible with each other. So the K60 120Mhz part should have the same mux options on PTE1 as a K70 120Mhz part. And a 2.x K60 100Mhz part should also have those mux options. (I linked to the datasheets for the specific parts on those boards). The only differences of course being instances like on the K70 where you also have an LCD option because only that chip has an LCDC module.
So if you are using a TWR-K60F120M board, then I would expect your scenario to work. Since it's not, it would not be because of the pin muxing but something else. Maybe double check the rest of your muxing and code to ensure it matches the correct K60 120Mhz datasheet.