Hi Darth, you say...
'From what I've read so far: when we hit a gust (up, increasing angle of attack) the 'plane will naturally want to pitch back nose down - due to the longitudinal stability. But my (rather limited) experience seems to suggest that the aircraft will want to pitch up and climb whenever we hit a gust.'
I think what it really means is that it will want to pitch back down -AFTER THE GUST- has occurred.
If you have gained height in the gust, you will have also lost speed, so the plane will be flying slower and producing less lift... hence it descends to increase speed, back to the previous level, and so the start of a phugoid oscillation... see chapter 6.1.14
For my Cessna 172 a stick induced pull up of 200ft resulted in a loss of 20 knots. Then when I released the stick the plane dived 300ft in 18s and regained 30 knots, then it climbed 200ft and lost 20kts in the next 18s, then dropped about 100ft and was just about back where we started from.
The relationship between speed and height is mentioned in chapter 1.2.1... Try to remember the conversion formula. It is very near 10ft/kt/100kts i.e. one division of the altimeter is equal to one division of the ASI at 100kts... but only at 100kts (it is half that at 50kts.). As one goes up the other goes down.