Can I skip applying the unallowed passive loss carryover (UPLC) from prior years for the year that I had no taxable income?

Yes, you can do that but it's important to keep track of that for future years. Keep your documents with your tax file so that you do not lose it.  

The suspended passive activity losses (PALs) can be used in only two circumstances:

1. Against passive-activity income
2. When you dispose of the passive activity in a fully taxable transaction to an unrelated party

Thank you very much for the reply.  You saved my day!