For a NASA study of just what you're suggesting:
http://gltrs.grc.nasa.gov/reports/1997/TM-107422.pdf
Note, the fuel was JP-10 (jet fuel, highly refined kerosene) and not a solid like you're describing.
Also, since you're in Iowa and one of the best groups for AM/EX rocketry is based in Quad Cities:
http://p209.ezboard.com/btqc
As for a fuel rich system that you could case, if you're going to be entraining outside air, it could be anything from HTPB (binder in most APCP motors -
http://www.aeroconsystems.com/misc/htpb.htm ) to paraffin wax. A good example of this is most of the hybrid rocket motors. They take things like PVC, vaporize them (via a pre-heater) add decomposing liquid nitrous oxide and you get rocket thrust. (N2O decomposes into (2) N2 + O2 at about 450°F)
The thing that I think will be your biggest hurdle will be to create a rocket motor within the ramjet that will produce enough thrust to get the ramjet up to speed to operate as a ramjet without fouling the diffuser/combustion chamber/nozzle of the actual ramjet. If you look at the width of most rockets and compare that to the width of the nozzle opening, you'll see that the nozzle opening will be too small to use for the ramjet. Here are a few examples from commercially available motors:
Aerotech I284W
http://www.aerotech-rocketry.com/custom ... m_assy.pdf
It has a grain width of 1.308" (33.2mm) with a nozzle opening of 0.266" (6.75mm)
Aerotech J1999N (800 pounds of thrust for 0.7 seconds)
http://www.aerotech-rocketry.com/custom ... p_assy.pdf
It has a grain width of 1.87" (47.5mm) and a nozzle opening of 0.713" (18.1mm)
In order to produce thrust to need to build pressure within the combustion chamber of the rocket motor. The only really way to do this is to restrict the nozzle exit (without restricting it too much) If you only wanted a fuel rich gas generator, an over-expanded nozzle on a APCP rocket motor would work as you'd never build up enough pressure to get a complete burn but it will not produce thrust.
The most common ramjet that I have seen is Decker's design. If you follow that design and have a diffuser entrance area of about 8 square inches you end up with a combustion chamber width of 6 inches. A combustion chamber width of 6 inches would call for a nozzle exit width of 4.5 inches and a length of about 3 inches and doesn't use a de Laval nozzle like is required for a rocket motor. Converting the nozzle to a de Laval nozzle is very doable and might even add to performance in some situations but the overall nozzle geometry for a ramjet is very different than a rocket motor.
Back to the biggest (and only really) hurdle is how to create a rocket motor within a ramjet that can generate enough thrust to move the ramjet to a speed high enough that the ramjet could then produce enough thrust to continue.
I don't really have any suggestions as to how to do that. Getting a liquid fueled ramjet that produces the desired thrust at the desired airspeed is hard. Solid fueled ramjets are harder. What you're suggesting is even harder yet.
-Aaron