Both Feeds are valid and it is not very important which Feed you have submitted to the iTunes Store. The iTunes Store and the iTunes client software will show only the posts with attached media files.
Which Feed have you submitted to the iTunes Store?
Because of the invalidation, iTunes removed my podcast from the store.
How do you know that? Did you get an email or an other message which contained this explanation?
Are you sure that it was not beacause of the title of your Feed (Doctor Who: Adventures in Time, Space and Music ? Podcast Feed). “Doctor Who” is maybe a term which is protected by some kind of trademark or seen as misleading because your podcast is as your description says it not The Doctor Who podcast.
and now when I ping, it seems to come up with
I don’t understand. What is comming up? The iTunes client software with the iTunes Store page of your podcast? How is that possible if you are sure that your podcast was kicked out of the store?
A different thing is the iTunes button of the podPress Feed Buttons widget. If I click on this button the iTunes client software starts and subscribes immediately to your podcast. The Feed behind this button is https://adventuresintimespaceandmusic.phillipwserna.com/feed/podcast . You are using the iptc:// option of the widget which makes iTunes start. But this works without submitting the Feed to the store.
You probably know how it works but here are the instructions on how-to submit a podcast to the iTunes Store https://www.apple.com/itunes/podcasts/specs.html#submitting
Regards,
Tim