I have found alternate fingerings a great way to work on "filling the gap"
for example - playing the high G on 1-3, then lifting the first valve while aiming to hold everything else )air pressure/speed, tongue position, embouchure) the same. The shortening of the tube will take you up to the next note, as opposed to going from open to 1-2 where you have to switch harmonic. (Please bear in mind that this is based on my very-likely-skewed perception of the laws of physics - but it works for me)
I've also recently started working on the "squeak-til-you-slot" method, but using glisses rather than scales, and this seems to be working really well so far.
- Adrian