How to connect 2 polysurfaces?

Hello there,
I am starting with Rhino. I have “designed” such a cradle:

The pointed by red arrows objects are not connected to the one pointed by the blue arrow. Because of that when I soften the edges, they are being softened for each red arrow object, also in the place they touch the base object- this I would like to avoid. So to fix this I was trying to join all these objects into 1, but keep failing.

How to achieve this end effect? I would appreciate all feedback!
I have attached my project file.

s10_samsung_charger_stand.3dm (375.2 KB)

Using Join will work only on the top parts, after that Boolean Union to connect the whole piece together into a closed solid

Thought I tried that… Anyways, worked just fine! I needed to join it twice (first for one side and then the other).