Shade Hangars
I could not do my Phase 1 out of SQL, so I moved my plane to Livermore. I ended up parked on the ramp in front of the tower, but toward the end of my stay (~3 months) there, they did offer me a shade hangar that had become available. So maybe there isn't one available now, but you can ask how long the shade hangar wait list is.
There is also a pretty active EAA chapter there. You might contact them and ask if anyone has some spare room.
But worst-case scenario you could get a cover and you'll be fine. I had to do the drive there every time with my car loaded with tools (or hundreds of pounds of sand used to Weight/CG testing). Get a truck-bed tool box and lock it to the tie down so you can leave most of the bulky and heavy stuff there. Not ideal, but really doable.