what's the value of having Googlbot crawling those parts of the old site that don't server 301 yet?
They stay (about) right where they are in the SERPs... There's no change to those, and the timing of events from start to finish, for me, would be totally Bot Dependent. As soon as a majority of pages, or even 'key pages' within a directory are crawled and the SERPs start to reflect the change I would move the next directory. What this does is help keep 'moving shock traffic drop' to a minimum.
It's been reported here (Bing especially) can at times take a while process redirects through the system to be reflected in the SERPs, so rather than having all the pages moved on a single day and maybe taking (up to) 3 weeks to see the new locations replace the old locations in the SERPs you can maintain a 'more consistent' level of overall traffic to the sites.
I would personally not worry too much about infrequently spidered pages, because they are probably not the 'substance' and 'traffic drivers' either, so if there were a few 'danglers' not spidered I wouldn't worry about it too much, because until they are spidered there will probably not be a significant change in the SERPs related to those pages either.
One of the reasons this method was suggested (to the best of my memory) was so you don't make the change on the entire site today, have all the old URLs removed from the SERPs and then have to wait for the new URLs to replace them over the next 2 days to 3 weeks...
Changes in the SERPs are not 'instant' so it might be your redirected pages get spidered today, tomorrow they start to drop lower in the SERPs and in three or four days (or more) they are replaced by the new locations in the SERPs. During this time the terms with the pages 'on the way out' and a new set 'on the way in' won't be sending the normal amount of traffic, so by staggering the move you can keep the overall number of URLs in the SERPs higher and not risk 'a day without traffic' or something to that effect.
I haven't done this 'site to site' specifically, but have done it 'intra-site' when changing a URL structure and although there was a % drop in traffic overall it was no where near where it could have been (IMO) if I had 3 to 10 days of very limited URLs in the SERPs...
Basically, when redirecting large portions of a site I 'rotate through' the directories at (generally) about 1 per week, so I might take a traffic hit on one directory the first week, then the second week I'll add another, but the first is starting to recover and so on...
Another thing you might want to do (I just thought of this and think I've heard it reported it's possible) is designate specific directories as sites in WMT so you can manage them individually, which should make it so you can designate them as 'moved to' there as you apply the redirects.
Another thing staggering does IMO is makes it so if anything goes wrong you don't have both sites entirely dropped from the SERPs at the same time... When you see the new URLs beginning to replace the old ones, in my experience, you can fairly reasonably determine the move is going well and move on to the next directory.
Anyway, that's probably how I would handle it, YMMV, and I don't know what would happen if you redirected everything at once from experience, because it's not anything I've ever tried... Any large URL changes I've applied have been on a directory by directory basis for years, and it's been quite a while since I've had to apply large scale redirects to any site, so I can't say for sure exactly how things are currently being handled.
The general, underlying reasoning for this type of move has nothing to do with whether the move will be effective or where the new URLs will eventually rank after the move is complete... It's all about minimizing the traffic drop during the move, and by spacing the move out and letting SEs find it in sections the traffic drop is, in my experience, spaced also, so you might take a % hit on the overall traffic to the sites, but it will be spread over time rather than a 'plummet and hope to recover soon' situation.
It's more about traffic management than anything, and the real timing I would use in making decisions on when to redirect each subsequent directory would be traffic and 'new URLs replacing the old' based... If I see the new URLs are replacing the old in 2 days, and traffic is constant I would make the moves closer together, but if I see traffic is dropping or the new URLs are not replacing the old quickly I might spread the timing out a bit...
Again, it's not about whether the redirection or move will be effective over time nearly as much as it is about managing the overall level of traffic to the two sites during the 'Search Engine adjustment and re-ranking period' for the new URLs (website).
ADDED:
Some of the timing I would use would probably depend on the specific situation and how many directories I had to move... If there were 50 I might move one a day for 50 days, and 'roll through' the transition rather than waiting as long between, so I would know for the next 60 days I'm probably not going to have my usual traffic to the sites, but the drop would be more likely to be a 'rolling % drop' than an all at once 'disappearance'.
For me it would really depend on the specific situation more than anything else, so it could be on a really large site I would simply make the decision to move one directory a day and get through the move quickly at the beginning, then I could adjust the timing as I saw the changes take effect and either bump it up to two directories a day or one every-other-day or something if things weren't going as smoothly as I would like.
Just remember once you make a move like this if you make it site wide, there's no 'undoing' it, but if you move in segments, you have some time to watch and make decisions, which is why I would probably do it the way I outlined going from site to site the same way as I have intra-site, but ultimately, the decision is up to you and what you are most comfortable with doing.