I have a similar setup on my test machine. I tried using a single home partition as you did, but ran into problems using the same username. I would suggest different usernames in each distro or eliminate the separate partition.
This laptop computer is my test computer. I have a deskop with only Linux Mint and Windows 10 that is my main computer. On the test computer, I don't have much in the home partition. I installed each distro on its own partition with /root on that respective partition. I didn't point the installs to the /home partition, but rather just save things there manually. They all share the same /swap partition. Originally I chose the 10 most popular Linux distros on distrowatch.com and proceeded to install them. I did have trouble with a couple that either wouldn't install or other errors, so I just moved on to the next one until I had 10 distros installed. So there were a couple of distros that gave me trouble and I moved on. I forget which ones they were. Currently my go to Linux is Mint Cinnamon.