OK having spent the last few days looking for the right solution here are my thoughts (for any Zune lovers migrating to WP8 who land on this post).
Firstly I don't think the Windows Phone App for Desktop has anything going for it. It's such a poor replacement for Zune syncing that persisting with it is an exercise in frustration.
Secondly, I should say that soon after posting here I updated to WP8.1 and WP8.1 has a built in podcast app. I have to say that as soon as I played with it I realised that part of my fondness for Zune wasn't just the managing-my-podcasts on a PC it was also familiarity with the old WP7 media player.
So the WP8.1 podcast app, with its familiar interface, is a good way to get on board with the idea of syncing/updating/managing your feed entirely inside the phone. Without having to learn a third party app.
Simple. Clean. Familiar. I was ready to fall in love.
However ... and this is a big however ... there are just too many feeds it won't play "An error occurred during media playback" (other podcast apps were happy to play the same file) and it doesn't reliably remember playback position. I'm not going to whine on because it could be those issues get fixed quite quickly - it's a very fresh new app/feature after all. But those problems do make the app unusable.
But this exercise did wean me onto the idea of using a podcasting app, even a third party one.
I've been trying Podcast Lounge, Podcast Critter, BringCast, iPodcast, Podcast! and some more. Not one of them, I'm afraid, as easy to use as the old player in WP7.
Podcast Lounge and Podcast Critter seem to be among the best. A special mention to Podcast Critter in view of my original question about organising large numbers of feeds and files. Podcast Critter does have the nice feature of grouping episodes by month (with each month available as a jump shortcut).