Been searching through old Price newspapers and, rather interestingly, it seems that the Republican Party tried to encourage an E.H. Cotter to run against Robert. Until recently, Cotter had been marshall in Helper and only a few months earlier had relocated to SLC where he was now working with a railroad wrecking crew. Anyway, Cotter seemed reluctant to leave SLC (his widow was still there in the 1940s) and that left RM the only Rep candidate, so he stood unopposed. Then Thomas Kelter (D) whupped him in the general election of autumn 1910. Mind you, Kelter saw off a succession of Republican candidates.
I put this timeline together through reading the newspapers available through the link you sent. Takes time to find stuff, but it's there. Will send a copy of Draft 3 very soon.