Proper wording: His or Him?

[crazyeye]

*Which pronoun works better, or is the sentence just awkward and better scrapped?

We had been rolling through the White Mountains for hours with his/him issuing these vague proclamations every seventy miles or so.

The proper noun works fine in that slot, but I use it in the previous sentence and prefer to avoid redundancy. Thank you.

[5jj]

We had been rolling through the White Mountains for hours with his/him issuing these vague proclamations every seventy miles or so.

Arguments about this sort of problem have been going on for a century or more. My personal feeling is that, in this particular sentence, 'him' is acceptable, and 'his' sounds very unnatural.