Fastest way to write 0x00 to a zero-page memory location? (6502, Atari 2600)

Question

I have a kernel in my 6502 game that writes two dots to a sprite, so for example:

........
........
.XX..XX.
.XX..XX.
........
........

Either 0, 1, or 2 dots can be on at a time. This is done one scanline at a time, so we're only looking at how to write the middle two lines.

So far I've implemented this by doing the following:

1. The accumulator is set to 0b01100000
2. X is set to 0b00000110
3. For the left dot, I use STA $1B (3 cycles) to only turn that dot on.
4. For the right dot, I use STX $1B (3 cycles) to turn that dot on.
5. For both dots, I can use the undocumented instruction SAX ($87) to write A | X to the value, so SAX $1B (3 cycles) to turn both on.

But if I need to turn both dots off, the quickest way I know of to write 0b00000000 to a register is to store $00 in Y and then write it. Of course, this means I can't use Y for other purposes in my code.

I don't need a trick that takes 3 cycles (4 or 5 are fine) but are there any possibilities, without consuming a register, to write 0x00 to a memory location in zero page on the 6502?

EDIT: The above description of the problem is incorrect (see comments). I actually set A=01100000, X=00000110, Y=01100110, and use SAX to write $00. The question as posed (writing 0x00 to a register without storing 0x00 in a register) is still answered in the replies.

Answer 1

My second bite of the cherry: another of the undocumented opcodes is SYA/SHY/SAY which will:

AND Y register with the high byte of the target address of the argument + 1. Store the result in memory.

If you were willing and able to switch your usage of X and A then you could have 01100000 in X, therefore the argument you supply to SAY would be 001b - b01100000 = ffbb:

9C bb ff          ; SAY $ffbb,x

So that would store Y & (ff+1) to ffbb + b01100000, i.e. it would store Y & 0 = 0 to 1b, in five cycles. Your Y can hold anything, and isn't affected.