The /tce directory, mount style extensions, are the preferred and default method for using Tiny Core.
However, that is not to say that using the advanced codes does not work...
Jonathan, likely two things that need to be done.
First when attempting to use local boot code then you should specify copy to file system, by using:
AppsAudit->Install Options->Toggle Default Copy Install
or, if you prefer from the command line touch /path/to/tcedir/copy2fs.flg.
Second when using AppBrowser, select the Download+Load option
or, from the command line, tce-load -wil extension
To your boot codes I would add:
waitusb=10 tce=sda1 opt=sda1 home=sda1 local=sda1 norestore
If you have edited/updated your /opt/.filetool.lst to include only those items outside of your persistence setup, e.g, particular files from the etc directory, then allowing a normal backup would make sense.
Following the above provides results as expected.