Well, as I said in my first reply, a podcast (the "subscription") is treated like a playlist, when you use the VoiceOver button (press and hold). On a playlist with songs, when you use play-in-order mode, the songs are played in order and then it stops after the last song. It does not go to the next playlist automatically and start playing songs on that playlist. So, it's the same with podcasts. When you select a podcast (instead of a playlist), the episodes of that podcast are played in order, and then it stops. It does not go to the next podcast. You need to select the next podcast, using the VoiceOver button, to play episodes from that podcast.
Since you confirmed it is doing what asked about, it is working "as designed" in this respect. What we need to figure out is why you can't get podcasts to play when you add them to playlists, which should also work as a way to play podcast episodes in ANY desired order (without having to switch between podcasts).
If you add items to your shuffle manually, by dragging them to the shuffle in iTunes, try doing the following:
Select the shuffle in the iTunes sidebar, under DEVICES. Click the small triangle next to the shuffle so that the shuffle's "content" drops down, indented under the shuffle. Right-click on the shuffle and select New Playlist. A new playlist should appear there, indented under the shuffle. Name it something appropriate, like "New Podcasts" (or whatever you want). This playlist will be only for your podcasts (no songs). You can create other playlists there for songs, if desired.
Drag the podcast epidsodes you want to hear to the shuffle in iTunes. Instead of dragging them to the "overall" shuffle, drag them to the playlist you just created. When you are done dragging podcasts to the shuffle, select that "podcast" playlist (under the shuffle). Over to the right, you will see the list of podcast episodes on that playlist. You should be able to drag the items around on the list, to change the playlist order; that is the order the podcast episodes will play on the shuffle.
When using the shuffle, set the power switch to play-in-order mode (not shuffle mode). Use the VoiceOver button (press and hold) to swtich to that playlist with your podcasts. It should play your podcast episodes in playlist order.
NOTE: If you are using automatic syncing to load content on your shuffle (you do not drag items to the shuffle in iTunes), please post back.