remember they'd only move around if they have to. if energy abounded they'd have no reason to move around.. but if you mean because they'd have nothing to push off of? well, assuming they need to crap and can hold pressure this crap vectored thrust would be adequate for impulse engines.. its the moving around at hypervelocity thats the snag, they could move between systems at their own pace if they were ageless.
given the incalculable amounts of energy being radiated by a star they'd have a home for its lifetime, only needing to move when the potential dropped dangerously low, the local space becomes too polluted or the star grows faster than they can move away [or can't stomach IR for elder stars]..
how better to create a dysons sphere than from the corpses of organisms that feed directly off of a star? if they keep reproducing and the LZH is thin enough that when they die the dead stay in relatively the same position without accreting [which though nice for fiction would be impossible outside of the stars planar spinning orbit (which could be radical and not as perfect as our old sol.. but i'm being convenient..).]
woot! i've been exoner8'd! no more infamy for me!!!

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don't call me skinny! i'm just ...

<<< ... aerodynamic!
its in my initials, an anagram.. seriously!