ZAB CTLR ISSUED WRONG ALT TO PHX ACR DEP AND EXPERIENCED OPERROR AT FL210 BETWEEN ACR AND MIL FLT AT BLOCK ALTS.

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I WAS WORKING THE RADAR POS OF SECTOR X COMBINED WITH SECTOR Y AT ZAB. I HAD BEEN ON POS FOR 2 HRS. FOR THE FIRST HR OR SO THE TFC WAS VERY LIGHT. ABOUT AN HR AND A HALF INTO THE SESSION; A D-SIDE CAME TO ASSIST. AT THAT TIME; TFC WAS ALSO KIND OF LIGHT. HE WAS TOLD TO ASSIST ME BECAUSE IT WAS GOING TO GET BUSY. I FELT IF IT WAS GOING TO GET BUSY; THE SUPVR SHOULD SPLIT THE 2 SECTORS. INSTEAD; HE KEPT THE SECTORS COMBINED. AT THE TIME OF THE INCIDENT I WAS WORKING ABOUT 17-20 ACFT. I HAD A STRING OF INBOUND ACFT; ABOUT 12-14; TO PHX (SECTOR Y) AND A MIL FLT OVER-FLYING WBOUND ON V190 IN THE BLOCK 220B230 (SECTOR X). I HAD ABOUT 4 ACFT DEPART PHX CLBING EBOUND ON V190. PHOENIX DEP ISSUES FL210 TO THEIR DEPS. THE FIRST 2 CHKED ON AND I RESTATED FL210. WHEN THE THIRD CHKED ON I WAS IN THE MIDDLE OF TRYING TO GET SPACING ON THE ARRS AND INSTEAD OF RESTATING FL210; I SAID FL310. A FEW MINS LATER; I NOTICE ACFT X CLBING OUT OF FL213. I THOUGHT IT MIGHT BE A MODE-C SWAP; BUT I IMMEDIATELY XMITTED FOR THE ACR X TO VERIFY LEVEL AT FL210. I XMITTED 3 TIMES BEFORE I RECEIVED A RESPONSE FROM THE PLT THAT HE WAS MANEUVERING IN RESPONSE TO AN RA. SHORTLY AFTER THAT; THE PLT OF THE MIL FLT STATED THAT ACFT Y HAD TO MAKE AN EVASIVE MANEUVER. AT ZAB WE ARE VERY SHORT STAFFED. ON A REGULAR BASIS; WE GET OVER 2 HRS ON POS. ABOUT 20 MINS BEFORE THIS INCIDENT; A COUPLE OF CTLRS RETURNED FROM BREAK AND INSTEAD OF MAKING THEM GET CTLRS OFF POS AFTER 2 HRS; THEY WERE TOLD TO DO SOMETHING ELSE. IF THE SUPVR KNEW IT WAS GOING TO GET BUSY; HE SHOULD HAVE SPLIT THE SECTORS INSTEAD OF USING A D-SIDE. THIS WOULD HAVE ALSO MEANT LESS FREQ CONGESTION. SUPPLEMENTAL INFO FROM ACN 766088: AS PM I WAS OPERATING THE RADIO. WE WERE LEVEL AT FL210 AND WAS HANDED OFF TO A NEW FREQ; WHICH CLRED US TO FL310. I READ BACK FL310 AND WE BEGAN TO CLB. AT 21800 FT IN THE CLB WE GOT A TCAS TFC ALERT; WITH NO OTHER GUIDANCE. WE WERE BOTH LOOKING FOR TFC BUT IT WAS NOT HARD TO FIND. AT OUR 12 O'CLOCK POS AND LESS THAN 2 MI AWAY WAS A FLT OF 4 MIL ACFT AT FL220. TCAS OFFERED NO GUIDANCE BUT IT WAS OBVIOUS THAT EVASIVE ACTION WAS REQUIRED. FO SMOOTHLY BUT FORCEFULLY TOOK THE EVASIVE ACTION NECESSARY TO AVOID A COLLISION. ATC SUPVR CONFIRMED VIA TELEPHONE UPON ARR THAT OUR CLRNC HAD BEEN TO FL310 AND APOLOGIZED FOR ANY INCONVENIENCE WE SUFFERED.