I've found some of the altissimo notes on bari can tend to be around a quarter tone sharp when using some of the same fingerings for altissimo notes on alto (eg. altissimo A is sharp on bari with the 8ve oxx|xxx fingering), so you will have to experiment with fingerings that are better tuned.
Not bari saxes (or any other saxes) but talking clarinet here - the altissimo A fingering (Sp.Th. oxx|ooo F/C) on clarinet should really be Bb, but because it's so flat it makes for a very well-tuned altissimo A.
If you've got a bari to high F# it does make some things easier up top as it will bridge the gap on some of the altissimo notes. Starting with G, you play it as high B with the high F# key open (8ve xoo|o high F# oo). G#/Ab and A you'll have to experiment with as all baris will be slightly different.
I don't know if having the doubled lower speaker vents on Yamaha baris helps with the altissimo but you can creep up from Bb by keeping the speaker key and LH3 down and using the palm and high E and F# keys opening them in turn (and keeping them open as you go up) to go higher, so Bb is with the high D key, C is with the high D and Eb keys, C# is with high D, Eb and E keys, D is with high D, Eb, E and F keys and Eb is with high D, Eb, E, F and F# keys.
Then a change in embouchure (ie. tightening it up) and you can start on altissimo E with the high D key, F with the high D and Eb keys, F# with high D, Eb and E keys, G with high D, Eb, E and F keys and G with the high D to F# keys.
And then again with an even tighter change in embouchure starting on G#/Ab with the high D key, A with the high D and Eb keys, etc. etc.