The only checkrides that you'll have a chance with are the CFI ones. Otherwise, inspectors are usually too busy to do Privates or Instruments. The only exception is when they have to do a certain number of "ride alongs" with new DPE hires, but even then they cannot technically ask you any questions.
The CFI initial though, there's your chance. It saved me about $400 to use a FSDO. I found the ride fair and actually pretty easy, although the fail rate is quite high.
When you call a field office, specifically ask to schedule a time for an inspector. Inspectors are told that if they cannot accommodate you within two weeks of your desired date, then they have to pass you along to a DPE.