Changed engine, heated ventilation smells oily

I had developed a habit of checking the oil of my 97 Tercel
just before long road trips. Recently, I had not made such
a trip for a lengthy duration. It turns out that the engine
had an oil leak, and it got run dry. The engine couldn't be
refurbished, so it was replaced by a remanufactured engine
with less mileage than the original one.

The engine had a horrible smelt that seemed like a cross between burnt
sugar and burnt rubber (if you've smelled burnt sugar from high
school, it doesn't smell sweet). It aggravates the throat, and I
cough for a day afterward. My eyes also water. The problem occurs
when I turn on the heater and get air from the outside via the vents.
It is not noticable at first, but becomes noticable after the engine
warms up (about 15-20 minutes). After it peaks, it seems to abate
slowly thereafter, though never seems to go away. When I turn the
temperature to cold, it is less noticable, but it is hard to tell
whether that is simply because the air is colder (it is winter here,
temperatures well below freezing). It is also hard to tell whether
the lingering taste/harumphing is simply lingering
physiological/psychological effects from when the air was hot. Note
that the winter environment ensures that the intake vents just beneath
the wipers are largely blocked with ice, so the air from the outside
is sucked from whenever it can be.

Two passengers of mine also found the odour quite noticable, though
they didn't seem much bothered in terms of breathing or watery eyes.
A car-savvy friend said that it didn't have to sweet smell of burnt
coolant. I guessed that it must be either residual coatings from the
remanufactured engine, or residue due to the overflowing power
steering fluid (I topped it off, and thought it might be overflowing
when heating up). I tried to burn off any residue by a day of heavy
driving, with the heater & fan fully on. While this diminished the
effects, they are still present and don't seem to be abating any more.
After this point, passengers did not find the odour significant,
though they still noticed it. It still causes me to cough for upto
a day afterward. At this point, I've driven the car for 2 weeks since
the engine was replaced. I thought that a fragrance emitter in the
car may be making the smell very confusing, so I removed it. Since
then, I've noticed that the smell is more like hot oil (possibly
burning oil, though I hesitate to characterize it that way).

My mechanic is pretty trust-worthy. I've been going to him for years,
and he has a reliable reputation in the community. He did not notice
any smell. I left it outdoors overnight, similar to my usage
scenario, and asked him to drive it for 20 minutes. He also found no
signs of leaks. He also said that the engine was not cleaned with
chemicals (or at all). I don't doubt that he doesn't find the smell
noticable, since he is exposed to much stronger smells in the garage
all day. I am also not surprised that him and others aren't much
bothered by it. I have been tested for allergies and been told that I
react strongly to mild aggravants. Furthermore, I am exposed to the
aggravant day after day, continuously, rather than for a short duration.
So it bugs memore, and I have a much greater interest in finding the
cause for this.

Can anyone suggest a next step for troubleshooting the cause for this?

Thanks,

Toyota Owner