Medieval Chinese Pronunciation
Middle Chinese starting from the Sui dynasty (with the Qièyùn, 切韻, published in 601 CE) actually documented its phonology. These are called rime tables, and break down each character pronunciation into groups by tone and by final. These were employed by scholars in both reciting and composing verse. Using the fanqie 反切 spelling would also have aided scholars in pronouncing characters.

However, the compiling of the Qieyun's pronunciations means that it is unlikely to have been one single system of pronunciation from the outset. It was a group of scholars, who appear to have come from both northern and southern dialect backgrounds, who helped compile the Qieyun. Hence some contest that, much like General Chinese would come to be, the Qieyun system was a diasystem across several dialects. Other see it as the general koine of Sui China as spoken among the educated elite across the nation. 

Kroll seems to have employed the Baxter transcription of Early Middle Chinese as based on the Qieyun. The monograph that outlines this transcription comes from his "A Handbook of Old Chinese Phonology". He does say that:


  The notation I introduce here is not intended as a reconstruction; rather it is a convenient transcription which adequately represents all the phonological distinctions of Middle Chinese while leaving controversial questions open. 


The transcription system itself seems to be fairly pronounceable; whether I would distinguish it from several other finals is another question. That transcription above, trhjowngX is composed of the initial trh-, and the final -jowngX. The initial corresponds to a retroflex aspirate stop (not affricate). The final is an open final of the mixed third division in the Middle Chinese rising tone. I'd personally go for something like [ʈʰjowŋ˩˥] if I had to give some kind of idea of its 'original pronunciation'. But it's not something that is recommended!

The one used in Schuessler's work is the Karlgren-Li reconstruction, although with a different convention for notation of the tones, the glottal stop, the e, i and w medials, and a modification of the "strong palatal medial" in fourth division chongniu. The actual differences between the Baxter and the Karelgren-Li(-Schuessler) are significant, but are structurally similar, based as they are on the Qieyun.