I just made a test pamphlet (although I have never done so before) with LibreOffice Writer and LibreOffice Draw just to see how it worked because I've never experienced what you're talking about. It seemed to work and print fine.

Here is how you do it in LibreOffice Writer:

1. Open a new document
2. Go to Format -> Page and change the "Orientation" selection from "Portrait" to "Landscape". Make sure you hit "Apply" before hitting "OK".
3. Go to Format -> Columns and change the number of columns to 3.
4. On the same screen as step 3, there is "Width and Spacing". In that section I left "AutoWidth" checked. Then I increased the "Spacing" value to 0.35". A different value may suite you better. Basically this is setting the space between the columns. Hit "OK".

This printed fine for me (although I didn't print it to a physical printer because I am not at the office, instead I printed it to a PDF document. This is different than asking LibreOffice calc to converet it to a PDF document. I have installed a PDF printer on my computer so I can literally select PDF as one of my printers). It sounds to me as if you have probably worked quite a lot on what you're doing and unfortunately probably started the process by trying to make a portrait document look like a landscape document. When you go to print, it prints like a portrait document because that's the foundation of what you have been working on.

The advantage of doing all of this with LibreOffice Writer instead of LibreOffice Draw is that it creates columns quickly and evenly for you so you don't have to fiddle with it much. The disadvantage is that Writer automatically starts moving content over to the next column if you add stuff to a previous column. So changing stuff in column 1 will also change things in column 2 and column 3.

An alternative option is to use LibreOffice Draw which is the open source answer to Microsoft Publisher (although I suspect it's not nearly as refined as Publisher). Draw is more like taking a blank piece of paper and drawing stuff on it. You decide pretty much everything. If you decided to switch to using Draw, you would have to create at least three text boxes representing the columns. You could move the text boxes around and position them where you would like. The advantage would be that anything you do with each text box would not affect the other text boxes. The disadvantage would be that columns would not automatically be generated but would rather need to be manually created and positioned using text boxes. I actually never use Draw so there may be a more efficient way to use it to create a pamphlet but that's how I did it just a few minutes ago.

With both Draw and Writer (or Microsoft Word or Publisher for that matter) you'll need to start off with a good foundation which means you need to start by switching the formatting of your page from Portrait mode to Landscape mode.