Keyword stuffing for SEO: when keyword stuffing is good and will help you and when it won't
Pretend that USA Today has a section of their site where the sell electronics, which they locate at http://electronics.usatoday.com. The subdomain is powered by an online electronics store called NewCo via a white label. Many of the pages on this subdomain have relatively high PageRank. But few, if any, external sites link to the subdomain--the PageRank of the subdomain is largely due to internal links from the usatoday.com root domain.
USA Today's deal with NewCo expires and they decide to partner with my startup instead. But, unlike NewCo, we won't be providing a white-label solution; rather, USA Today will be redirecting all of the electronics-related links on their root domain to my site instead of the electronics.usatoday.com subdomain. They also agree to direct all of the pages on electronics.usatoday.com to me.
Ideally USA Today would add 301's to all of their pages on electronics.usatoday.com that direct to the corresponding pages on my site, but they don't have the engineering wherewithal or resources to do this. Therefore, what is the best way to pass the PageRank from the electronics.usatoday.com pages to my site? Would it work to have USA Today change the CNAME for electronics.usatoday.com to my site and then create pages on my site that mimic the USA today URL structure? For example, let's say there was a page located at electronics.usatoday.com/ipods. Could we give electronics.usatoday.com a CNAME form my site and then create a page on my site located at mysite.com/ipods that 301'ed to the ipod page on my site? Would that preserve the PageRank?
The absolute best solution is to use 301 Redirects to map every one of the old URLs to a new URL. If this isn't possible, berate and plead with the appropriate developers/administrators until they put 301s in place. Don't take 'it's not possible' for an answer: it's always possible.
A second-best solution would be the canonical tag. You would have to keep all the old pages, but add a canonical link tag in the head section of the HTML. This now works cross-domain.
A CNAME like you mention is a third option, particularly if all the old content has completely gone. You would point olddomain.com to newdomain.com, then on newdomain.com you can handle all requests for the old domain and show appropriate content. Again, you should add the canonical link tag to point to your own copy of the page on newdomain.com if it exists.
What you described is probably the most likely way to proceed (in terms of reducing tech overhead).
The problem comes from the fact that it's been stated that every 301 redirect doesn't transfer 100% of PageRank - that some decay occurs. This is further exacerbated when you chain redirects together, as you're describing.
However, this is an issue that can only be mitigated, not prevented altogether, and as long as the new links are correctly linked to from the parent site - direct, not via 301s - then you'll soon have new PageRank flowing to offset that lost by the migration.
How many pages in total are you talking about?
What is the nature of their inability to add 301s? If it's just a matter of writing down exactly what should go in the htaccess, you can do the legwork and show it to them, right? I've often observed that some clients feel like they can't be bothered with being involved at any level once they start paying for a service. But that's ridiculous. If they can be made to see that doing 301s is necessary, they'll find a way. They are 'USA Today,' after all, not some dinky local paper.
But to the issue at hand. You could perhaps settle this by using canonical tags. And a few years ago, very short (eg, zero seconds) meta refreshes were passing pagerank… though I haven't done that in a while since the other options are better.