Storing/deleting photos using cloud, phone, and mac

I just recently purchased a new macbook and am using the cloud to share my photos between my iphone and my computer. The problem is, I'm almost out of room on my phone so I'd like to move the pictures off my phone, to my computer, and still have them available in the cloud. I can't find a way to do this.

I went through the process of downloading all 6,000+ photos from the cloud to my mac (selected the "Download Originals to this Mac" option in the photo app on my mac). However, the minute I delete a picture from my phone it deletes it off my Mac, even though I'd downloaded the originals to the computer.

I then disabled the cloud feature for photos on my mac. I was then able to delete a photo on my computer and have it stay on my phone. However, the minute I reenabled the cloud feature for photos on my mac, the photo disappeared from my computer!!

This shouldn't be so complicated - I should be able to download all photos in the cloud to my computer and then delete them off the other device they live on and have the photo still live on the computer and in the cloud. What am I doing wrong???