Please don't confuse Bleed Trips with Pack Trips.
Bleed Trips are triggered by high temperature or high pressure in the Bleed Ducts downstream of the engine (measured in engine pylon). The only air this single heat exchanger feels is engine bleed air so any object plugging this would have to go thru the engine core. A journey it is not likely to survive or not leave a permanent mark on the fan. These trips are MELable with major operating restrictions, ie "no known or forecast icing, and single pack ops only. These Bleed Trips can be reduced to single events if proper T-shooting is followed. This requires special measurment tools and time so that part is easier said than accomplished. Once the shotgun is broken out and the suspect parts are changed in inverse diffulculty order you (the operator) are doomed to many nuisance trips.
Pack Trips can be caused by many faults but plugged heat exchangers are not usually one of them. Each pack has two heat exchangers and the inlet for these is on the under belly just aft of the forward cargo door. this is one with major airflow into it when you are going under the wing to check the tires. These heat exchangers can be plugged by airport environment trash but are usually just dirty from dust, dirt and I suspect primarily "SMOG". If one of these heat exchangers is plugged you will usually see it as "Ram Air Door Full Open" light on at top of descent. this is also fully MELable with minimal restrictions.
If you are in a position to influence your "25 year old engineers" than encourage them and their management to fully follow the Boeing FIM before shotguning the easy parts. This will require management to schedule the airplane into maintenance where the people, tools and most importantly the time are available.
SEAMC out