I just found something interesting in the GMRS rules. From 95.1771:
a. Each GMRS transmitter type must have the capability to transmit F3E or G3E emissions.
b. Only emission types A1D, F1D, G1D, H1D, J1D, R1D, A3E, F3E, G3E, H3E, J3E, R3E, F2D, and G2D are authorized for use in the GMRS.
Ok. F3E is FM (frequency modulation) voice. G3E is phase modulation voice; essentially the same as FM. So basically a. states that a GMRS station must be able to transmit FM.
Then, b. adds to that. In addition to being capable of transmitting FM, a GMRS transmitter (because the transmitter is really the regulated part) may also have the capability of transmitting the other listed emission types. 1 and 2 refer to digital content. 3 refers to analog content, including voice transmissions.
The third character refers to type of content, with E being telephony: voice or music. Of course music is verboten, so E means voice in the case of GMRS.
So looking at the first character, the analog voice modes that are listed are: A3E, F3E, G3E, H3E, J3E and R3E. As already stated, F3E and G3E are FM voice.
Here's the interesting part: A3E is AM voice. J3E is SSB voice. H3E and R3E are modified forms of SSB. DSB (Double Sideband, suppressed carrier) also falls under the heading of A3E, so that would be allowed as well.
Conclusion: as long as a transmitter meets the rest of the requirements (including the ability to transmit on FM), there is nothing prohibiting the use of SSB or AM on GMRS. If someone would just build a Part 95 type classified multimode transceiver...
The thing is, on ham radio it is not uncommon to communicate over paths of hundreds of miles, simplex, using 432 MHz SSB. It would seem that availability of a proper radio is the only thing preventing us from doing the same on GMRS freqs.