I have never smelled a clutch related issue that had a sulfurous odor,
but who knows?

Actually, I suspect you have a problem with your catalytic converter
or related system.  When you are starting up and pulling away, the
emissions system may be overloaded with gasoline (rich) which can
cause sulfurous gas to be produced.  That is my best guess, anyway.

The key concept here is that you're slipping the clutch, which *ALWAYS*
causes heat. The secondary concept is "it just started doing it", which
indicates (at least to me) that you're probably due for a fresh clutch
disk and/or flywheel/pressure-plate resurfacing pretty soon - Likely due
to you slipping it. Unless you can't avoid it, slipping the clutch as
you describe is to be avoided as much as possible, for exactly the
reason you're seeing. (err... smelling)

How many miles on the clock? You say you've had it 2 years, and its a
'00 model, so I wouldn't doubt that it's getting close to time for a
clutch job anyway, particularly if you regularly slip it as described.
No telling what the previous owner did to/with it, obviously, but it's
possible that (s)he was another clutch-rider.

A good rule is to always get off the clutch pedal as quickly as possible
- The quicker the disk is solidly mashed against the flywheel by the
pressure plate, the quicker the disk can dump whatever heat built up
during the most recent operation to the flywheel, instead of retaining
it and cooking itself.

If it's a 2000 car then chances are it has 80,000 to 100,000 miles and
the clutch could be worn out.  The way I test a clutch is to drive up a
grade in high gear, hold the gas pedal down and press on the clutch
until it starts to slip and release the clutch pedal.  The engine
should immediately slow down to operating speed.  If it takes more than
an instant then the clutch is for sure going bad.

However, cars can emit several different smells, so you might want to
have it evaluated by a good repair shop or Suzuki dealer.

[ snip ]

That could be your problem right there! If your RPMs can, in any
reasonable, or even conservative sense of the phrase "really high", be
characterized as "really high" while you are slipping the clutch, you
have a slight problem understanding clutches and respecting their
limitations. You need adjustment, not the clutch.

Under worst case circumstances, you don't need to go above 2000 RPM,
nor slip the clutch for longer than 2 seconds. I will probably get
flamed for suggesting such outrageously high numbers, too.

Take some lessons. Get into your car with some expert who will tell you
what you're doing wrong and how to do it differently.

During parallel parking moves, you only make brief touches with the
clutch to get the car to roll. The clutch quickly comes up to the
friction point, stays there very briefly, and then comes right down all
the way! In other words, the clutch is disengaged most of the time.
This is true even on an incline. Use the hand brake to hold the car
when starting, and a combination of hand brake and gravity to stop it
from hitting the car in front.  The downhill moves are just done using
gravity; no need to engage the clutch at all, nor even to change gear
from forward to reverse or vice versa.

Sure, this stuff is mildly difficult, but you sign up for it when you
get that manual car.  Part of the fun is constantly monitoring your
technique and striving to improve. People who don't want to monitor
their technique in controlling a sensitive machine, and strive to hone
it to perfection, should not drive manuals.

If you've been abusing the clutch for as long as you've owned the car,
no wonder.

This is confusing. These two smells are nothing alike. A fart does not
smell like something is burning. Farts smell due to the presence of
hydorcarbons with -S-H groups (sulphur, hydrogen). If it's like rotten
eggs, it's likely the catalytic converter. But your description is
ambiguous; nobody would describe that as burning. Maybe you have both
smells going on at once.

It could be that you get nervous when you are doing these parallel
parking moves, and have a gaseous bowel movement from the tension
without noticing it.

Exactly. You get scared, and blow one. Is that "rotten eggs" component
of the smell more prominent if you sample the air nearer to the seat
cushion?