An adjective of number, a superlative or an emphatic adjective that describes the antecedent is often put in the relative clause (or "attracted to the Clause of the Relative", as Kennedy phrases it). The adjective will agree with the relative pronoun.
si veniat Caesar cum copiis quas habet firmissimas
if Caesar comes with the strongest troops that he has
librum quem recentissimum habebat mihi dedit
he gave me the newest book that he had
So, the position of the adjective is entirely normal. Thus, I would put universum with gaudium – universal joy (pace Evan T. Sage who has evidently translated it as an adverb!).
Given that a comparative (quam) +/- a relative pronoun + the subjunctive suggests a result/consecutive clause, a literal translation could be:
there was a universal joy so great with the result that the men
couldn’t accept it
or more polished:
there was universal joy greater than what the men could accept
Ref: Kennedy's Revised Latin Primer, p.156, point 332, note 2; and Colebourn, Latin Sentence and Idiom, p.115, point 375; and Morwood, Latin Grammar, p. 100, point 6