I thought to translate this way too, except I read ἐπειδὰν + aor. as after
but you can saywhenever they have finished + verb
to give both the general sense of subj. and anteriority of the aor.
Those datives gave me a hard time until I decided on pretty much the same meaning as yours.
With λέγει ἐπ' αὐτοῖς ἔπαινον τὸν πρέποντα I had troubles, specifically I thought λέγει ἔπαινον has the meaning ofto praise
and then the articular part. is the direct object (one person among those buried who is distinguished/suitable
to receive said praise), but it's actually as you read it, an articular adj. for ἔπαινον, for all the buried.
Then I checked myself with the 1910 translation @Perseus, and they loosely read ἀξιώσει as a noun and προήκῃ as its adjective,to be the first in worth/reputation
= of eminent reputation
; however, they read γνώμῃ not as going with μὴ ἀξύνετος
but with δοκῇ, to be considered in their opinion to be wise/intelligent
= of approved wisdom
There are notes by E.C. Marchant (1891) about ἀξίωσις worth noting:
Grote and Shil. say ἀξίωσις means the estimate one has of oneself; ἀξίωμα that which others have of one.
Such a wide difference does not exist here. ἀξίωσις is the recognition of a man's γνώμη.