There are two basic types of gyros. Rotational gyros do just as the name implies, it measures rotation but cannot give you an orientation. This type is not appropriate for your job.
The other type senses G-force. Now how does that help? Well, if you've a sensor which senses G-force in two perpendicular axis, like the AXDL202, that tells you the absolute angle in relation to gravity:
Ch A faces up, B faces left/right:
Ch A= 1g, Ch B=0g: straight up
Ch A= 0g, Ch B=1g: lying on its side, right side up
Ch A= 0.707g, Ch B= -0.707g: heeling 45 deg, left side is up
It's solid state, tiny, can be waterproofed easily, no wiper noise, will never wear out, and has no lag or "swinging" action. You can get samples for free from Analog Devices. I think you can get an eval board free too so you don't have to etch one. If not, I know I've seen eval boards for that part on eBay.
They also have a PWM duty cycle output in addition to an analog output, which gives you two ways to interface with a PIC.
IMHO Stamps are junk. They took an older PIC, used its own onboard nonvolatile memory meant for the user assembly program to make a BASIC interpreter and threw the program on an external chip. Made it 10x-100x slower and then raised the price 10x-20x. Very pointless, the PIC is meant to store the program in its own memory. Use the chip with 2 external components and you're done. There are C compilers so you don't have to write assembly. You need to buy a programmer, about $100, but look at what you save not buying a single STAMP. Or you can make a programmer pretty cheap too.