A brief passage in Tongdian, a Tang dynasty encyclopedia, reports a Chinese soldier's impressions of life in early Abbasid Iraq (where he found himself captive after the Battle of Talas): Tongdian, chapter 193. A translation, taken from Hoyland (1997), is available online: T'ung tien. Unlike many of the other foreign accounts of early Islamic history that Hoyland gathers, which tend towards the bitter, this text is in parts rather charming, particularly where based on first-hand observation. However, the transliterations are as unhelpful as usual. Here are the appropriate Middle Chinese forms, based for convenience on Starostin's database, with y substituted for j:
T'a-shih: 大食 thầyźik, a reasonable transcription of Persian Tājīk, itself originally from Arabic Ṭā'ī (member of the tribe of Ṭayy) - see Language Hat)
mo-shou: 摩首 mwâśǝ́w – no idea what this alleged title of the caliphs might be; probably not Arabic, so maybe Persian? Any ideas?
Po-ssu: 波斯 pwâsye "Persia", presumably from Pārs.
Fulin: 拂菻 phütlim "Byzantium", apparently somehow from Armenian Rhôm (ie "Rome").
Ya chü-lo: 亞俱羅 ʔạ̀külâ "Kūfah", a pretty good transcription of the town's Syriac name, ʕAqūlā.
mumen: 暮門 mòmon (given as a title of the caliph), ie Arabic mu'min "believer"; the vowel choice in the second syllable is interesting, suggesting that the short i was already pronounced in a rather schwa-like way.
Shan: 苫, ie Arabic šām "Syria, the Levant, Damascus". This character isn't in Starostin's list, but its Korean and Vietnamese readings make it clear that the final letter was m, not n (CJKV-English dictionary).