ZDV ARTCC CTLR LOST SEPARATION WITH 2 ACR B757 ACFT ON CONVERGING COURSES AT FL350.

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I WAS WORKING 3 SECTORS COMBINED -- LOW ALT; HIGH ALT; AND ULTRA HIGH ALT. WORKLOAD WAS HIGH; BUT NOT OVERLY SO. WE WERE REQUESTING AND RECEIVING ELT RPTS (EMER LOCATOR XMITTER). ABOUT 2 HRS EARLIER; WE LOST BOTH RADAR AND RADIO CONTACT WITH A PIPER CHEROKEE NEAR ALAMOSA; CO. I HAD 2 LOW ALT ACFT IN THE GENERAL VICINITY OF THIS LOSS. I REQUESTED THEY BOTH MONITOR 121.5 FOR THE ELT. THERE WERE SEVERAL HIGH ALT ACFT ALSO. I RECOGNIZED A CONFLICTION BTWN ACFT X WBOUND FROM OVER ALAMOSA TO FARMINGTON; NM; TO LAX; AND ACFT Y NWBOUND FROM OVER SANTA FE; NM; TO FARMINGTON TO SFO. AT THIS TIME; THEY WERE EACH APPROX 100 MI FROM FARMINGTON. I WAS WORKING THESE SECTORS COMBINED BECAUSE WE DID NOT HAVE ADEQUATE STAFFING TO OPEN APPROPRIATE SECTORS TO LESSEN WORKLOAD. I WAS TOLD I HAD 19 ACFT ON FREQ. THAT WOULD BE ON 3 FREQS DUE TO LACK OF FREQ COVERAGE. WHEN THE ACFT WERE ABOUT 50 MI FROM FARMINGTON; I ISSUED A 35 DEG L TURN TO ACFT X. HE READ THIS BACK CORRECTLY. IN MY EXPERIENCE; THIS WOULD BE SUFFICIENT. I THEN WENT ON TO CORRECT A HDG GIVEN TO AN ACFT Z ON HIS WAY TO RAZOR BACK; AR. AT THIS TIME; A LIFEGUARD KING AIR POPPED UP ON FREQ REQUESTING AN IFR CLRNC TO ALBUQUERQUE. I ISSUED A CODE FOR HIM TO SQUAWK. I THEN RECOGNIZED THAT THE ACFT X AND ACFT Y WERE GOING TO GET WITHIN 3 MI OF EACH OTHER. I TOLD ACFT X TO TURN ANOTHER 15 DEGS AND TOLD ACFT Y TO TURN 20 DEGS L. IT WENT FROM 5 MI TO 4 MI TO 4.3 MI BACK TO 5 MI AND GREATER. THEN I CLRED THE LIFEGUARD TO ABQ; SHIPPED A COUPLE OF ACFT AND WAS PROPERLY RELIEVED FROM THE SECTOR!