[cabmandone]

A few things:
1. You say it's not near the low end of temperature rise. What is the temperature rise? Again measure Supply temp at main trunk after the first duct going to a room vs return temp at furnace? It would also be nice to know what your ambient air temp is in the home versus what your return air temp is. Again this will tell if you have any cold air infiltration.
2. You mention yellow flame. Does your unit have an inducer fan that runs prior to the unit lighting? I'm guessing an 87 will have in shot burners with no air adjustment. Are you burning propane or Natural Gas? The yellow naturally indicates incomplete combustion. A small amount of buildup on the burner orifice can create this, You can usually use a flashlight and inspection mirror to see the ends of the burner orifices.
3. As for how far a bird can get, if you have an inducer/purge fan, not very. I have cleaned them out of the purge fans on several occasions.

Post some pics of your burners. I would be interested to see the cooked goo you're describing.

Also don't want to be an alarmist but yellow lazy flame can indicate a cracked/plugged heat exchanger. If you don't already have one, get a Carbon Monoxide detector in your home. Also make sure the tech puts a Combustion Analyzer on the unit and does a CO test