SudokuSolves/FizzBuzz

OP = Pallando

A Fizz Buzz solve path:

Using the blue and green diamonds only, get me as far as:
https://f-puzzles.com/?id=yhfdne4s

Looking at the 9 in box 5, the light greens are possible 3s and the
light blues are possible 5s.

There are at most 4 possible 3s, which means we need at least 5 5s.

Box 6, 8 and 9 between them can give at most 2 5s.
Which means we need at least 3 5s from boxes 2, 3, 4 and 8 - if we can
elliminate even one of those as possible, it fixes a lot...

Looking at the red 6 diamond in box 1, it can have 2 fizz at most,
meaning it needs at least 4 buzz. Which it can potentiall get from
boxes 2, 3, 4, 5 or 7 - so, again, elliminate one of those
possibilities and we're sorted.

I've put circles around the key squares I'm interested in elliminating:

https://f-puzzles.com/?id=yfycdxlk

Now for a cunning bit of logic:

I've noted that r4c5 and r4c6 are the only possible locations of a 3
in box 5. And that r9c5 and r9c6 are the only possible locations of
a 3 in box 8. Therefore, either 2 of them hit the 9 or neither of
them do. And if neither do then there are not enough 5s able to hit
the 9. So it MUST be 3s in r4c5 and r9c6:

https://f-puzzles.com/?id=yeowjnmc

Looking at the 7 diamond in box 1, there are certainly at least 2 and
no more than 3 threes hitting it, meaning there are 4 or 5 5s hitting
it. If they come from boxes 4 or 8 they can only come from the
circled light blues in those boxes, which even it none of them get
elliminated still leaves 2 or 3 to come from boxes: 2, 3, 4, 5 where
they'd have to come either from the light blue circle in box 3 or from
one of the cells I've circled in red:

https://f-puzzles.com/?id=ydmmklgx

Looking at the blue 2 in box 9, we note that 3 of the 4 red circled 5s
hit it, meaning one of them can't be a five. So, to complete the 7
in box 1 the only way for the red circled 5 in box 2 not to be needed
would be if there were 3 3s on the 7 in box 1, which would require the
3 in box one to be in r2c1 but that, in turn, would leave the green 1
diamond in box 1 without a 3 pointing at it.

SO, THEREFORE:

r1c5 _is_ a 5.

From there we have several routes. We can do more jiggery pokery
with the 2 and the 4 in box 9. But perhaps the easier path is to use
standard sudoku naked and hidden singles, which takes us to:

https://f-puzzles.com/?id=ydjtj56n

and flipping back and forth between the logics takes us comfortably
the rest of the way.