Hi there
It will take a bit more time, but rewriting the content to be unique would be so, so worth it.
If Google notices that you're syndicating content with dofollow links to your site within them, it will think that the only reason you're doing so is to pass more PageRank to your site. It won't think that you're offering as much worth to the other blog and subsequent referrals if you're regurgitating what has been said.
Now, the obvious exception to this rule are Press Releases through sites like PRWeb. This is a well-known anomaly in the industry (some say it passes juice, Matt Cutts tries to say it doesn't), but it's so far down the line now that it seems unlikely that Google is going to penalise your site for it. The worse that would happen would be not passing any SEO value.
It is not safe to assume that this would be the case for sending your articles to these other blogs - it may very well penalise you.
By rewriting the content, you negate any risk of this and also ensure that the uniqueness will most likely pass the SEO benefits from the separate blogs.
To me, it's a matter of risk management, and all signs seem to point towards rewriting the content. It's a bit of an annoyance, but a small price to pay considering the benefits. It's also a great compliment to what you've written before, which has obviously proven to be very valuable, so congratulations on that!