The squeal might be coming because of dust clogged inside the motor. Are you sure the noise in not coming somewhere from the cabinet?

Lining the return chase will make it quieter and if some of the noise is air, increasing the return will help with that. The material used to line the duct must be fireproof. I know of no return grills that set flush with the wall. The stamped face grills only set out 3/16", may 1/4". If you wanted the grill to be recessed, you could cut the hole to accept the grill to fit into, then frame around it.

Ok thanks for the suggestions. The motor that came with the brand-new furnace had a very loud hum continuously (and it ran hot) ... a real high-quality made in Mexico motor. The installer replaced it with a (made in USA) GE motor and a new starting capacitor. It's made the exact same noise for almost 11 years. It wouldn't be such a pain if the furnace weren't installed in the middle of the 1st floor of the house.

I have encounted this problem with Miller HVAC units before as well as some Gibson and Tempstars. The HVAC cabinet usually vibrates due to the fan motor. Possible solutions are, 1. Does the unit "suck" the closet door closed when it kicks on. Like if you open it about two inches does it suck it shut? IF so, enlarge the return air vent. This will make a unit louder than it needs to be because it is restricting air flow making the unit work harder. 2. Acid clean the coils (spray foam available at most bigger home improvement stores. Also, pull the squirrel cage and clean the dirt off of it. There will be some built up on it possibly throwing the cage off balance. This will lession air noise due to cleaning off dirt that got past your filter that could be obstructing air flow. 3. Replace the rubber gromments holding the motor to the cage if they are dried out. Oil the motor with regular SAE-30 car oil. About 15 drops per oil hole. (there normally is a metal or plastic plug on each side of the motor on the edge of the casing. A dry motor will make more noise, waste electricity and eventually burn up. I am always amazed at how many motors get burned up due to not being oiled on a regular basis.. Only need oiled one to two times a year. 4. Re-Tighten the squirrel cage to cabinet mounting screws. They loosen with vibration and eventually start to hum real loud. If all else fails, and it is completely driving you insane, consider having a secondary return duct ran. It is simple if your unit is a downdraft split unit, It involves putting in a floor mounted return filter grill ( which means cutting a hole in the floor, running a flex duct back to the air handler closet..) Not too hard nor too expensive if you do it yourself. Expect to pay a HVAC tech about $250-$300 or more to do this. Some may be cheaper, but very unlikely. If you are lucky, the rear side of the closet may face another room.. If so, relocate the return air to that side and close off the vent in the other side. Just cut a hole in the wall carefully, install a return filter grill like you will find at the hardware store and then go close off the other side. Having secondary filtration always helps in the long run. James