I managed a work around - full actions below. Some or all may be necessary, this is just what worked for me.
Firstly: Apple...? Is there an official response to this? When can we expect a real fix? It shouldn't be arcane. If we have a check box that says a file is going to be synced, it should be synced - or we should be told it cannot and why. It should just work. If it is complicated under the hood, the software should hide that from us.
What I did:
Unchecking and rechecking didn't work for me.
I tried to make it as simple for the system to honour my requests as possible:
* I deleted all podcasts from my phone, and as far as the phone is concerned, it isn't subscribed to any, and it has none listed. I did this to avoid any conflict logic that may be happening when it tries to determine if a specific file should be synced or not.
* In iTunes, I check the specific podcasts I want to be synced to the phone using the 'sync podcasts' checkbox but not the 'automatically include' checkbox. Again, I did this to reduce any logic issues that may be happening when I tell it what I want to sync to the phone.
After a sync, there are still no podcasts on my phone.
If I look at the 'on this phone' tab in iTunes, it thinks they are on the phone (they are greyed out, with a dotted circle next to them, but they are listed and they each have a checkmark)
That lead me to look up what the dotted grey circle meant. Seems that is a a mess all of its own. Basically, it indicates files it know you want to sync, but can't (lack of memory? DRM/license issues? Because it is Friday? Who knows)
The fix for this was to check 'manually manage music and videos' in the summary tab in iTunes.
Hope this helps.
I want to reenable the auto logic at some point as I'd like to listen to a new podcast episode without always doing a hard sync to my computer - but for now, I'll accept this.