Hi Matt,
Yep, those are probably the hardest notes to get. There's a couple of ways to approach them. You can "half hole up", from the note below, or close holes lower down. With the low F#, you can't really close enough holes to get it in tune, but one way is to also half close RH1 - the hole you work with your right index finger.
I've been experimenting with the little black rubber widget / thingy that they supply to allegedly switch to German or more sax like fingering. I've found I can fit that in RH1 instead (it's meant for RH2), and it does a better job of half closing it than I've been able to do with my finger. You could try that. Either think of it as training wheels, or maybe just leave it in there semi-permanently. It flattens some other notes, of course, but it's only really noticeable on G.
With my current weapon of choice, a Yamaha 7C with a #2 Rico Plasticover reed, I can bend the G up to pitch without having to think about it much, with the widget left in RH1.
It can only affect notes you finger with that hole open, of course, and it has less effect on A than on G (really not an issue) and even less on B than on A. I'm not suggesting it has to be there, but it is an easier way of making the low F# more playable, than trying to get it just right with your index finger. Mostly, it proves it can be done. No doubt, you could learn to do it without the widget, once you get used to it.
For the G#, half holing up from G isn't too bad, though I find it hard to hold it stable. Half closing RH1 helps with that too (with or without the widget). I have a couple of other variations, which I'll come to shortly.
For the first octave Bb, I can think of three main ways. Neither of them is perfect, so any of them will do, depending on which is easiest at the time (i.e. depending on where your fingers were on the previous note, or need to go next).
a) Half hole up from A (i.e. partially open LH2 - left middle finger) and optionally close RH1 and RH2.
b) Use the register key thumb lever as a Bb side key, raising an A fingering to Bb. Optionally close just about any combination of RH1-RH3 - more for stability than tuning. This one's a bit weak and weedy sounding, but not bad for tuning.
c) Play it like a low C#, but with your middle finger off LH2 - it's a bit like a recorder fingering for that note, but with more holes closed below it. It may be a touch sharp, but I find I can scoop down enough (maybe harder with the 4C).
For the second octave Bb, the recorder fingering works really well - start with the A fingering and add RH2 and RH3, so it looks like this:
TR XXo oXX
(TR meaning thumb hole is closed, register key pressed, X = finger closes hole, o = hole is open)
Oddly, the recorder fingering for a B doesn't work, at least not for me, but I can improve on the one on the chart - play a B, but add RH1:
TR Xoo Xoo - and you may need to blow a bit harder, as with a recorder. It's hard to play that softly.
For the top C, the official one sort of works, but adding RH1 helps keep it stable. Adding RH2 still works, so that's another option.
Not on the chart, but the top C# isn't that hard. There's at least a couple of ways, but try adding RH1 and RH2 to the official C fingering, and optionally adding LH3:
TR oXo XXo or TR oXX XXo
I can sometimes get it to do it just by taking my thumb and all fingers off, but it does tend to fall on the floor

Holding it with RH2 works about the same. I can't do it consistently though.
The top half of the second octave can also be played as overtones, in roughly the same way that you can do it on a flute - i.e. use a fingering based on a note that's a fifth lower than the note you want to play, put more of the reed into your mouth so more of it can vibrate, and just try to get the overtone. Some are harder than others, so find an easier one first, then try to go from that to ones near it.
You might think that meant you can stretch it past the C#, but I haven't been able to, so far. Let me know how, if you manage it
So, here's a rough fingering chart, with some alternatives. I'll leave out the ones that work okay as they're written on the chart. I did this with the widget fitted in RH1, so when you see a h there, that's what I mean. Where you see a h for any other hole, I half closed it with my finger.
Venova fingerings - mostly, just differences from Yamaha's chart, and some alternate fingerings
h = half hole, or fit the fingering adapter plug / widget (in RH1 or RH2)
H = one black key rather than both together (e.g. as for D#)
R = thumb register key or lever
T = thumb on hole - which it almost always is
() = optional, i.e you can close that hole if you want to, but you don't have to
(Starting from low C)
C-E as on the official chart
F T XXX Xho / T XXX XoX / T XXX Xoo X
F# T XXX hXh / T XXX hXo / T XXX hXX (H) / T XXX hXo X
G T XXX ooo / T XXX hoo with bite to bend up (if using it with h plug / widget in RH1, to help get the low F#)
G# T XXh hoo / T XXh ooo? / T XXh XXo X / T XXh XXX X
A as chart
Bb T Xho (XXo) /
*TR* XXo (XXX or XXo or oXX) - mostly A + register key, with optional right hand fingers / T XoX XXX (H) (scoop)
B as chart or T XoX XXX H
C as normal but maybe add more RH fingers? Or T XoX XXX X
C# as chart (recorder, thumb open) / - XXX ooo / - XXX hoo
D as chart (scoop) / T XXX XXX (bite, not lever) / - Xoo hoo (easy trill with B) or possibly - Xoo ooo
D# as chart / TR XXX XXX
E as chart
F TR XXX Xho / TR XXX XoX
F# TR XXX hXo / TR XXX oXo
G as chart / TR XXX hoo (bite) / T(R) XXX XXX X (Overtone of C)
G# TR XXh XXo / T XXo XXo (H) / T(R) XXX XXX H (Overtone of C#)
A as chart or TR XXo XXo X / T(R) XXX XXX / T(R) XXh XXX (Overtone of D)
Bb TR XXo oXX (bite) / T XXo XXX / T XXo hXX / T(R) XXX XXh (Overtone of D#)
B TR Xoo Xoo blow! / T(R) XXX XXo (Overtone of E - tricky) / T(R) XXh XXo (Overtone of E - better)
C TR oXo Xoo / TR Xoo XXo (bite) / T(R) hX(X) XXo
C# T(R) oX(X) XXo / TR ooo (oXo) (not on the chart but definitely playable)
One last thing - the register hole, which the thumb key lever opens, is very small, so it gets clogged with water quite easily. A good way to clear it is blowing up the nose pipe, while pressing the register key to open the hole. Oboes have the same problem, but they don't have a conveniently placed pipe to blow through... Maybe they should.