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I'd recommend working on it in reverse, slurring from the G to the F. Make sure you are buzzing the individual pitches and not just hoping that the horn will do it for you. Also try using a half valve slur.

Roger

You want to know an "Arnold Jacobs explanation?" You are trying too hard. Don't use too much tension. Seek the ease in playing.

F to G is only a whole step but by habit, and through your technical knowledge that F to G changes overtone series, you are exerting too much tension to change a whole step. 1) Practice blowing the air without buzzing, while fingering F to G. 2) Practice going from G down to F, keeping your airstream steady and supported and unchanged. Seek perfection in this easy drill. 3) Begin to combine repeated G down to F pairs together, making sure the tongue is not involved. 4) Repeat the same process with F to Gb. 5) It takes several weeks to instill a new playing habits, so spend a few minutes doing this everyday.

You might also look at low Bb to C (and Cb) and well as an octave high Bb to C.

Good luck, make music and enjoy.