How can I stop Firefox adding more and more tiles to my New Tab page?

Question

The New Tab page in Firefox lets you add tiles for your main shortcuts. I like this feature and don't want to turn it off, but there's one aspect I want to disable if possible as it's very annoying.

I like to keep just a few tiles on the page, but Firefox keeps adding more and more, apparently using it as a kind of history dump. For me this defeats the object. The page is very cluttered instead of having my chosen few main links standing out.

I was able to limit the number of tiles by setting browser.newtabpage.rows to 2 and browser.newtabpage.columns to 4 in about:config. This gives room for enough tiles for me, plus a bit of space at the end for when I occasionally want to add another one. However, Firefox still won't stop filling up that bit of space at the end. Worse, it stacks up an immense number of "hidden" tiles that are waiting to come onto the page, and as soon as I delete the last tile to make space for my new one, Firefox fills the space again with the next "suggested" tile.

I can find no way to change the URL of a tile, which I expected to be possible by right-clicking the tile to set its properties, but it seems not: I have to sit there deleting the "last" tile over and over again, until I've exhausted Firefox queue of tiles and it finally leaves a blank space for me.

How can I stop Firefox adding tiles to my New Tab page?