Long story short I have more than enough space on my laptop to download my whole Apple Music library (which isn't very big at all) for offline play, but I have <1gb of space on my iPhone. Is there a way to download songs for offline play on my Mac without having it also download them to my iPhone (both which obviously use the same Apple Music account)?
Apple doesn't make you download on both systems, you can store them in the cloud.
Select all the songs in iTunes on your mac, right click and select download. Those will only download on your Mac. If you want to download some or all on your iPhone then you will have to click the cloud icon for each song or an entire playlist to start the download there.