If you only need to do this occasionally I suggest selecting the
column with the big gaps, including the header and in the drop down menu :
Data|Filter|Autofilter
Then in the dropdown list  which appears in the header cell choose
'(Non Blanks)'. This will hide all the rows with blanks in. Copy the
column to somewhere else in the sheet, or another sheet, in any event
avoid copying it on top of the hidden rows. Incidentally, it might be
safer to have no space between the quote marks at the end of your formula.

I'm actually setting this up for someone else, who is very nervous about
using the computer at all. I'm therefore trying to make it as automated as
possible for her.

Thanks also for the comment about the blank spaces between the quotes: is
there a quick explanation as to why this is better?

"is there a quick explanation as to why this is better?"

Note I did say 'might be safer' and that it was an incidental comment.

I just like things to be what they seem. As much as possible if a cell
looks empty I like it to be empty so that I don't have to start
considering 'What if there are invisible characters in there - how
shall I handle them? How many invisible characters are there in that cell?

The procedure I described using '(Non Blanks)' treats cells with just
a space in, in the same way as empty cells. So it doesn't matter there.

It is just a matter of preference.

If I get a moment I will address your chief problem.

>>If I get a moment I will address your chief problem.

I've now gone with my original messy solution, as I had to get it done, but
thanks anyway for your interest and time.