So unetbootin does not support upx'ed kernels. However, you should be able to use Tiny Core's usbinstall to get a working pendrive that does,
Result with stick created with usbinstall on a desktop machines:
Type h - works fine on desktop PC, 'Boot error' on Aspire notebook
Type e - works fine on desktop PC, boots on Aspire but freeze randomly
Type z - 'Boot error' on Aspire known from past experience, not tested now
This indicates that issue is not UNETBOOTIN specific.