PVT TWIN TURBOPROP IN SINGLE PLT IMC IFR OP EXPERIENCES ALT OVERSHOOT IN CLB ON MISSED APCH FROM GUP.

Narrative

I WAS ON AN IFR FLT PLAN IN IMC CONDITIONS ON A RWY 24 GPS APCH TO THE GALLUP; NM ARPT. AN ACFT PRECEDING ME ON THE APCH MISSED; AND I WAS CLRED FOR THE APCH. THE PRECEDING ACFT INDICATED THAT THEY HAD INTERMITTENT GND CONTACT IN FOG AND BLOWING SNOW ON THE APCH. CONDITIONS WERE RPTED AS 3/4 MI VISIBILITY; 700 FT CEILING. I THEN ELECTED TO FLY THE APCH AND WAS CLRED FOR THE APCH BY ZAB WITH INSTRUCTIONS TO RPT DOWN-TIME TO THE PRECEDING ACFT OR MISSED TO ZAB. AFTER COMPLETING THE APCH; I TOO MISSED AND BEGAN TO FLY THE PUBLISHED MISSED PROC L TURN AND CLB TO 8500 FT. AT THIS TIME; I WAS SEQUENCING MY GPS (A KLN90B) TO THE MISSED POINT FOR HOLDING; WHEN 1 OF MY 2 PAX CAME INTO THE COCKPIT TO ASK WHAT WAS GOING ON. I ASKED HIM TO RETURN TO HIS SEAT; ATTEMPTED REPEATEDLY TO CONTACT ZAB AND ENTER THE HOLDING PATTERN; ALL WHILE TRYING TO KEEP IAS ABOVE THE MINIMUM IN ICING CONDITIONS. IN THE PROCESS I CLBED THROUGH THE MISSED APCH REQUIRED ALT OF 8500 FT. I CORRECTED BACK DOWN TO 8500 FT; WHEN I FINALLY MADE CONTACT WITH ZAB. ABQ GAVE ME A 110 DEG HDG; 11000 FT WHICH I READ BACK AS SUCH. LATER ABQ INFORMED ME THAT THEY ONLY CLRED ME TO 10000 FT. A SECOND SUCCESSFUL APCH WAS CONDUCTED. THE PRIMARY FACTORS CONTRIBUTING TO THE ALTDEV WERE A VERY HIGH WORKLOAD IN POOR CONDITIONS AND A PAX DISTR.