Did you consider installing each of your systems with just the hard drive attached that will hold the system.

Only drive A inserted to install windows.
Only drive B inserted to install ubuntu.

After the installation is done you will then be able to select the system you want to boot inside of your BIOS boot order selection.
The running OSs will later pick up the secondary drive as unreadable (in windows) or as NTFS formatted drive in Linux.
When, during update-grub, the os-prober runs its code, it will add the windows system to the grub boot menu with a relative path to your grub mbr. Then you might fix the boot order to always boot from the linux hard drive, because grub will run (chainload) your windows boot loader.