Robert_Charlton - 8:35 am on Aug 4, 2013 (gmt 0)
...put an ordinary dofollow href link on each page of the old site with the anchor text "This site (or page) has been moved -- Click here to go to the new site (or page)".
Most visitors will click the link to go to the new site. And the links will also transfer most of the "pagerank juice" to the new site, but shouldn't transfer any of the penalty.
IMO, this has got it backwards. If there were direct traffic I wanted to preserve but the site had a backlink-based penalty, I'd put a nofollow link on the page. Seems to me that if the link passed PageRank, it would also pass the penalty.
I'd definitely not 301. JD_Toims is correct that a short meta refresh is likely to be counted as a 301. I've got no opinion about whether a meta refresh of any kind, either short or long, would pass a penalty, but I'm not sure I'd want to experiment in this kind of situation to find out.