Why might a passenger jet fly at altitudes in a strong headwind when the winds are more favorable at a different altitude?
You assessment is flawed in that it does not take different air density in account.  You state the following conditions:


FL320
80 kt headwind
355 kt groundspeed
1000 nm distance


and you are proposing descending to the following conditions:


FL220
40 kt headwind


At 32,000 ft, standard conditions are around 275 hPa, 225 K and density of 0.43 kg m$^{-3}$.  If your 80 kt wind is a pure headwind, a 355 kt groundspeed translates into a 435 kt TAS. If we correct this TAS for the ambient conditions we get an indicated airspeed of about 255 KIAS.  This is the airspeed that really matters because it is what the airplane experiences as it interacts with the atmosphere.

If we descend to FL220, where standard conditions are 430 hPa, 244 K and 0.61 m$^{-3}$, an airspeed of 255 KIAS yields a TAS of 363 kt TAS.  If we have a headwind of 40 its, this yields a groundspeed of 323 kt.  This is about 30 kt slower than you were flying at FL320.  A flight of 1000 nm will take about 15 minutes longer to complete.

However, it is most likely possible that the airplane you were in is capable of flying faster than 255 KIAS at FL220 and in fact is probably capable of somewhere around 310 KIAS.  Flying at 310 KIAS at FL220 will have true airspeed or 440 KTAS and with the 40 kt headwind a ground speed of 400 kt. This will get you to your destination faster, but at the expense of a much higher fuel burn. 

It is also likely that you could have been flying faster at FL320 (not sure what max mach number would have been for you), but also at the expense of burning more fuel.  If the airplane wasn't dispatched for the additional fuel burn to go faster at FL220, then after descending you would probably not have enough fuel to go fast enough to make up the difference in true airspeeds.