ANSWER FROM THE INSULATION DOCTOR:
Starting with the balloon walls. If they are true balloon walls which it sounds like they are they will be accessible from the attic. This means they are open to the attic. Therefore, you can either pour insulation such as zonolite or you can blow-in cellulose insulation. (If blowing in insulation you need to cover 90% of the top of the opening so the insulation stays in the cavity.)
Regarding the attic insulation, the carpet has no insulation value. It could cause other problems such as mildew and condensation, etc. I would recommend removing it by cutting it into strips so that it is managable.
Regarding the insulation in the roof rafters, this could cause two different problems. First problem is it is important to maintain a 1" airspace between the under side of the roof and the upper side of the insulation. Normally this is obtained by putting in a baffle or "proper vent". The second problem would be if the insulation is the standard blanket-type insulation with a kraft-backed or paper vapor barrier, this type of barrier does not meet any fire codes and could be a hazard.
Regarding blowing in insulation without a vapor barrier, your options are to cut 4-mil visqueen and lay it between the joists or add an extra R-value to compensate for the lack of vapor barrier. Generally we would recommend adding an extra R-10 to compensate for the lack of a vapor barrier.
Hope this helps.
Bruce Jones
The Insulation Doctor