A Latin Question

From 8th grade through college I took nine years of Latin and four of Greek, so even though that time is fast receding into the past, I generally consider myself up to figuring out Church Latin pretty well, with the occasional help of my Collins Gem pocket dictionary. (For such a tiny thing, the Collins Gem is pretty much the most useful dictionary you can have short of Lewis & Short. It looks a little silly sitting next to Allen and Greenough's Latin Grammar, but it's worth every penny of the 6.95 it costs you.)

However, as MrsDarwin was prepping the introit for next Sunday the other night, I found myself confronted by several difficulties. The introit is: Populus Sion, ecce Dominus veniet ad salvandas gentes: et auditam faciet Dominus gloriam vocis suae, in laetitia cordis vestri.

The first thing that struck me as a bit odd was the veniet ad salvandas gentes construction. "ad" normally carries a meaning of "to or for", but using a verbal adjective "salvandas" seemed a bit odd. By the details of verbal clauses are one of those things that's probably fading in my memory, so although I wasn't sure that this was a very classical construction, I had a rough idea of what it was saying. Literally it would be something like "come for saving the peoples". The translation of the gradual gives "come to save all nations".

Am I right that that's a bit odd, or am I just forgetting stuff?

However, when we come to the second half of the sentence we really go crazy on the verbal clauses. "et auditam faciet Dominus gloriam vocis suae, in laetitia cordis vestri." Conjunction, subject and verb are all pretty easy: et Dominus faciet -- and the Lord makes/does.

"vocis suae" clearly go together as singular genitives -- "of his (reflexive referring back to Dominus) voice"

"auditam" could be a future subjunctive first person "I shall hear" or it could be the feminine singular accusative of the verbal auditus, -a, -um. I'm taking it to be the latter, since we're about to run into a second person pronoun in the next bit, and so throwing in the first person seemed very strange. Thus, auditam goes with gloriam and is something like "hearing the glory of his voice". This would fit in with faciet, which can take a verbal clause as something that an agent allows or ordains.

However, we have complications, because next we get "in laetitia cordis vestri." which is pretty simply "in the joy of our heart".

Please tell me this is at least a bit odd? Or have I simply lost my classical mind?

The best I can come up with is something like "The Lord makes your hearts rejoice, with the glorious sound of his voice", but that's working completely at gut level and invoking the principle that "facio" can mean just about anything.

UPDATE: American Pheonix put up a post specifically to answer this, and cites the relevant Wheelock.