Slackware 14.2/current and Debian9/10 Live CD/USB with ability to be remastered into your own flavor, persistent, ability to boot to ram, operates basically as Slax.
These "flavors" of Slackware and Debian can boot off CD, DVD, USB, and Hard drive with persistence, toram, and can be on any fat32/ntfs or ext2/3/4 formatted filesystems. You can install frugally to hard drive or do a full install as a normal linux install.
Using the Live scripts found in /root you can make your distro any way...