Update: Tried it again with a non-encrypted persistent partition, and it works correctly. Persistent partition is mounted at /lib/live/mount/persistence/sde2. And once again, the media is mounted at /lib/live/mount/persistence/sde1. And it's mounted read/write (for root only). Files, including system files, get saved on the persistent partition, but root can write to the mounted media.
An unrelated problem: These images aren't booting properly. I'm being dropped to the syslinux boot: prompt because of two errors. If I enter the label ("live" or other label from the menu) then it boots. One of the errors had to do with chain.c32, and when I removed the harddisk entry from the menu, that error message went away, but it still dropped me to the boot prompt. I haven't tried to see if putting this entry back into the menu causes the problem again after fixing the second error.
The other was a problem with vesamenu.c32. I'm creating the live usb on a wheezy system, and I get the same result whether I use refracta2usb-0.9.6 or refracta2usb-0.9.6+sid1. In either case, the file is coming from the isolinux folder inside the iso, and these are jessie/sid images with a newer syslinux package. When I copy vesamenu.c32 from my wheezy installation to the syslinux folder on the usb stick, it boots properly (I get the syslinux boot menu). I'm guessing the problem is a mismatch between vesamenu.c32 from sid and ldlinux from wheezy.
I'm not sure how long this problem has existed. In previous tests with sid isos used on a usb stick, the stick always had a wheezy image on it first, and I kept the syslinux folder, thus keeping the older vesamenu.c32. I think this is the first time I've put a jessie/sid image on the stick first.
Not sure of the best way to fix this. Maybe need to do a version check of syslinux on the installed system and if it's older syslinux with the newer vesamenu.c32 issue a warning and/or give the option to copy the old vesamenu.c32 to the live-usb.