Since there are no answers, I will at least post what I have gotten so far:
The as.bugs.array function in the R2WinBUGS package was created for this purpose. According to the documentation (?as.bugs.array):
Function converting results from Markov chain simulations, that might not be from BUGS, to bugs object. Used mainly to display results with plot.bugs.
Thus, it is possible to obtain a plot from LINE.out in your example, although it does not plot the correct variables:
plot(as.bugs.array(sims.array = as.array(LINE.out))
It will take a little bit more work to figure out the correct way to transform the LINE.out, and the LINE.samples object from example(jags.samples) may be an easier place to start.