I think your equipment needs to be straightened up. I have no idea how you use it on its side.
I found that in CA and AZ, rust wasn't an issue. My son, however, in northern CA, found that rust is an issue.
Right now, I do all my reloading in the house and all the dirty jobs (case cleaning and gun cleaning) in the house as I am tired of reloading, freezing in the winter and sweating in the summer.
If you keep a light coat of oil on the press (and leave it covered by a sheet) and leave the dies in a box with DESICCANT, you will have no problems.
Rusty dies, actually, are seldom a problem. I have a couple and the rust is on the outside and the inside contact surfaces are rust free even after over 40 years of use. I really think the burnishing of the working surfaces and residual oils keep the working surfaces rust free.
If you worry, then move the clean reloading activities inside where you can maintain 55-90°F temperatures and 0-80% RH.