Is there any way to force the Startup Manager menu to appear on every boot? Rather than me having to remember to hold down Alt if I want a different OS.
I'm not sure this is possible by default without holding down the ⌥ key at startup. You can make the Boot Camp partition always boot by selecting it in System Preferences → Startup Disk, but it sounds like this isn't what you want.
You should then be able to select whichever OS you want to boot from there.
You don't without modifying things on a low level. When a mac can't find the first viable image to boot, you get the prohibitory icon - not the boot picker.
Intel Macs have the following basic behavior at boot time when the chime indicates a successful POST. This is the hardware behavior and unless you rewrite the code / replace the hardware, you are bound by this functionality.
The only deviations from this are when you press one of the startup key combinations to alter this list.
So, you can:
I don't know of a good guide to the last bullet point, but internet fame awaits someone (perhaps you!) that figures a nice way to hack a mac to show the boot screen as you ask.