I work with spreadsheets where I have to copy a value into the cells down a
long blank column next to another long row.

How do you highlight the range of cells to copy into?

I thought you could also highlight a blank cell (A) and a filled cell (B) to
anchor, then hit shift and down arrow to get a full range a1...b1000, then
move the cursor from B1000 to A1000 to get only the A column to paste into...

Does that question make sense?