Actually, he tried. He was in poor health at the time according to the application, though, and I am sure that it did take information a while to travel in 1909. There were two people who testified on his service in company E; W.E. Morgan and J.P. Andrews, which was on Aug 16, 1909. The War Dept on Sep 10, 1909, stated he was not on the rolls as Z. F. Elliott. Again, he was listed as Frank Elliott, not Z.F. or Zimri Franklin Elliott.
The 34th is not mentioned anywhere in the app, but I will search it out more, esp if W.E. Morgan or J.P. Andrews are listed, as well.
Thanks again for the help.