I've just been placing the objects mathematically by using an excel spreadsheet.
First, I divide the horizontal space by the number of objects.
Then I take the X-axis position of the first item and add to it the result of the division.
This gives me the X-axis position of the second item. Add the division result number again and I have the X-axis position of the third item. And so forth.
Do I have to say this is time-consuming? It seems there should be a way to do this with a few clicks
Have a look at the Align panel. There are distribute options there as well, including distributing the space between objects, or distributing the edges or centers of objects.
Just one more instruction is needed: Find the Align panel hidden at the end of a non-intuitive sequence: under Window, then Object & Layout.