It's a question somehow unanswered for a fairly long time, while it doesn't seem to be too complicated to answer.
If I am reading a Chinese text to a Japanese audience, how can I know which reading to use for each character? Of the 音読み, there can be 呉音, 漢音, and 唐音 to choose from.
There are two major types of situation to read Classical Chinese text in Japanese you might encounter: buddhist sutras, and all others.
In the latter case, it's usually recited through 漢文訓読, where all untranslated words (= remained as 音読み) are read prescriptively in 漢音 (though the rule was established relatively recently that there's no assurance older documents before Meiji conform to it).
兄弟
(brothers)
- everyday: きょうだい (both in 呉音) 「うちは三人兄弟だ」 My family has three brothers. ("I (who's male) have two brothers / I have three boys.")
- 漢文訓読: けいてい (both in 漢音) 「人は皆兄弟有り」 Other men all have their brothers.
Anyway, in most cases you don't need to practice the method first-hand, unless you are an enthusiastic Japanology researcher, because almost all of well-known texts already have translations, and what you have to do is just follow the textbook.
The buddhist sutras, on the other hand, are read as is and the pronunciation differs roughly between sects and schools. The largest portion of them use 呉音, but according to here and here, 天台宗{てんだいしゅう} has some 漢音 sutras, and 黄檗宗{おうばくしゅう} (a Zen sect) uses 唐宋音 in every piece.
南無阿弥陀仏
(Namo Amitābhāya)
- 呉音: なむあみだぶつ
- 漢音 (天台宗-style): なもあびたふ
- 唐宋音: なむおみとふ (Compare to Contemp. Mandarin nāmó ēmítuófó)
観自在菩薩行深般若波羅蜜多時照見五蘊皆空度一切苦厄
- 呉音: かんじざいぼさつぎょうじんはんにゃはらみたじしょうけんごうんかいくうどいっさいくやく
- 唐宋音: かんつざいぷさへんしんぽぜぽろみとすちゃうけんういんきゃいくんといちぇくえ
(Again, compare to Contemp. Mandarin guānzìzài-púsa xíng shēn bōrě-bōluómìduō shí zhàojiàn wǔyùn jiē kōng dù yīqiè kǔè)
Note that sutras contain many Sanscrit and Pali transcriptions that often deviate from dictionary reading of kanjis.
Also for pronunciation, would rhythm be modified to stress individual characters in deference to their monosyllabic origin in Chinese speech?
Yes, in buddhist tradition. In this YouTube clip you'll notice that every character (syllable)
is pronounced in the same length.