Hi, you need to give us more details on what you want and what have you tryied so far. Because this question seems a little OT.

In any case, here are some pointers on what I would do in your situation.

• On the hosting question, try Web Hosting Talk, it's a forum with good reputation as to hostings recomendations and/or previous troubles with some hosting providers
• To get the content from your previous host, and if you only have web access, you can use wget to retrive your content (not a Perl solution, but it is a good utility). If you have ftp access, I think you may better look for an ftp mirror module/utility (I use lftp, which have a nice mirror command, but YMMV).
• In any case, you need to ask you hosting provider to give you a tar ball of the full contents of your site. Because if you use wget, WWW::Robot or anyting else to retrieve your site with only web access, you will not get the full content of your site (not to mention that if any part of your site is dynamic (ie. CGI Perl or PHP based), you will loose your scripts and the actual data they use to present the content).
• You need to clarify what you mean by in-place editing. Is it Wiki, CMS? Or DAV, FP or DW extensions? Or something else? Because it is impossible to guess. ;)
• Your new host should provide a way to upload files, it can be ftp based or via cPanel, but if not, you need to begin looking for another provider right now. ;)

And just as a final note (because I am going way OT in this answer), you need to double-check with your provider about this:

The web server unfortunately doesn't have in-place editing...

Because if it means that you don't have CGI or PHP scripting or something, you will be very limited and may be unable to provide dynamic content on your site.