The literal translation of the sentence is:
"He thoroughly read the tablet, that had been received with the highest reference, and gave thanks to God."
What is unclear in the sentence is of course by whom the tablet had actually been received. I suppose this is because of the passive meaning of the perfect participle (although it does generally seem to be regularly used as being active in meaning), and the absence of an active participle.
The only error in your translation really is that you have translated 'acceptam' as being a present participle, rather than perfective, i.e. the tablet has been received and is then read; it is not being read while being received (a very tricky thing to do).
“Cum ego verbo utar,” Humpty Dumpty dixit voce contempta, “indicat illud quod optem – nec plus nec minus.”
“Est tamen rogatio” dixit Alice, “an efficere verba tot res indicare possis.”
“Rogatio est, “Humpty Dumpty responsit, “quae fiat magister – id cunctum est.”