Justin,
most of the solvers, except rk and euler, are able to handle stiff
systems, see the following table:
http://desolve.r-forge.r-project.org/slides/tutorial.pdf#24
Sometimes, tuning a few options may be necessary, e.g. specific settings
of atol and rtol for individual state variables, or choosing specific
method flags for lsode.
The use of lsodes with root finding is somewhat exotic and I guess that
nobody tried this before. Anyway, we will work on it, thanks for your
report.
Thomas