Can I speed up a 301 by getting external links to my 301'd pages so Google will spider it faster? I'm thinking of links from blogs, social media sites / bookmark sites etc.
Not clear exactly what you mean by "speed up a 301." It sounds like you've changed domains and want to eliminate the legendary time delays. If this is the case, in my experience, one thing you can do is to get as many of your old links changed to the new domain as you can.
This would suggest to Google a continuity of ownership, which might be important if they are to trust that you're not just buying up old domains for their inbound links and then redirecting them.