This may be a silly question, but ...
 

If I have a blog or site with unique content and I move that content to another blog or site, the new site will initially be seen as being a copy and penalized.

But, if I delete the original content, maybe replacing it with a link to where it was moved to (and assuming the content has not been scraped and copied elsewhere) will the new copy eventually be seen as having authority or will it be perpetually branded as a copy despite the original being deleted?

I'm considering migrating a blog I've put a lot of effort into from a free host to my own hosting, and thus cannot do a 301 redirect.

If there is your free host copy and then your paid host copy then there should not be significant penalty, however if it has been scraped and there are many copies of it on the web that could be problematic.

Personally I would move the posts to the new blog, removing them from the old one over time, don't do it all at once, make it a progressive move.

A permanently moved redirect would be better though.

Well, if there is a just one copy of a content it can be duplicated.

if you do it progressively google may penalize you for duplicate content.
I would add a ROBOTS tag to the old blog (revisit every day), and remove the content right away. Then add the content to the new blog.

Thank you for your insight.

It has well over 1000 posts, so maybe 10/day for the next 3+ months?

I'd hate to have all that effort go down the drain just because I decided to move it when I would have been better off leaving it where it is.

So 1 person saying gradually, and another saying all at once.

Looks like I need more folks to weigh in to get a general consensus.

Why don't you leave the existing blog where it is, seeing as it is free, then just continue on at your new blog ?

That's the problem with SEO related questions, there is no consensus.

Ask 10 SEO experts the same question and see how many different answers you get, I would expect you would get 10 different answers.

FWIW, I am no SEO expert, I only go from my own experiences, your mileage may vary.

I have a feeling with the Panda update we're going to see a lot of the free hosts pull up their stakes and pack it in. If it were a splog that wouldn't be much of a concern, but this blog in particular represents hundreds of hours of work and I want to be pro-active in case my hunch proves correct.

Ok, then my advice stands, move the content gradually by removing it from one site and replacing it on another, keep an eye for swings and roundabouts in your keyword ranking as you move the content, then if all is good, move more, but I would not do it all at once.