Changing RSS feed for podcast...all the tags are there but isn't changing?

You have buried the redirection tag inside the 'description' tag:

<description><![CDATA[A podcast dedicated to the show Doctor Who with a perspective from two Midwest United States Fans, and one person being introduced to the Doctor for the first time.

<itunes:new-feed-url>http://feeds.feedburner.com/travelvortex</itunes:new-feed-url>

]]></description>

This has rendered it invisible to iTunes. You need to move the redirection tag so that it isn't enclosed by any other tags except of course for 'rss' and 'channel'.

Evidently you tried adding it in the entry area for the Description. If you can't edit the feed directly then you can't add the tag and therefore can't set up redirection.

In this case you are rather stuck, and have only two options. The first is to abandon the old feed altogether. You should get the old podcast removed from the Store - instructions at http://www.apple.com/itunes/podcasts/specs.html#changing - and submit your new feed as an entirely new podcast. You will probably need to make a small change in the title, as a bug in the Store software may tell you that the podcast has already been submitted: and of course you will lose any subscribers or comments.

The other option is somewhat uncertain. iTunes Support is notoriously unhelpful, often sending back form answers which often don't deal with the actual problem, or referring the questioner to the Discussions Forum (which may have sent the questioner there in the first place): however it has been known for someone to persuade Support to shift their podcast to a new URL, so it's worth trying. It's probably just a matter of luck who you get. To contact iTunes Support, go to http://www.apple.com/support/itunes/ - click on 'Other iTunes Store Features' in the list and then on 'Podcasts'.