I was finally able to beat my previous score, grabbing every speed boost I could find helped a lot but it seemed like sometimes they just weren't there or were so far away that I never saw them.

Thank you for trying again. Your new score pushes you up to rank 10! :-)
The items are distributed randomly over each dungeon. But the total number of them is always the same. Since the levels are quite big there is a certain possibility to have no items visible on screen. However there are tricks to somehow enhance your field of view. E.g. you can often walk a "V"-shape through rooms. This will not cost you anything compared to moving straight because of your ability to walk diagonal. This allows you to pan your screen and maybe discover an upgrade. I would recommend the video of ToneHack since he explains a lot of tricks.
Hello nobusawa,
there is a new version of RunToTheStairs:
Please consider to play again!
Gerhard