It's possible with LP, but I doubt it's the heat exchanger.
I would be looking at flue gas recirculation, due to faulty concentric flue, or something with the intake?
Have you had the roof replaced lately? I've seen roofers cut the cap off of concentric kits, pull flue pipes right out of the draft hoods, etc... Mangling them so they could get a new flashing on.
Hard to say without testing it myself. What ever you do, it's time to ditch the old service company.
"The only true wisdom is in knowing you know nothing" Socrates