I smoke mine for about 3 hrs. till temp is 135 and delicious tender greatness.

Both are relatively tough cuts, the eye even more than the bottom, I think. A long long braise of some sort is called for. I would be inclined to cut it up as stewing beef rather than keep it whole. We raise beef ourselves, and those are two cuts I always have ground into hamburger! Good luck.

The eye & bottom round are from the same part of the round called the goose neck. Personally, I feel both are better braised, but can be roasted, if not cooked more than medium rare. Both cuts have very little flavour, since both do not offer much marbling.

/eye of round is a little more tender. The CI method really saves it, but you still need to slice thinly. I did a modified version of the CI method and it beat conventional roasting hands down.
http://www.foodsville.com/recipes/view/309

And here is their guide on tough cuts.
http://www.cooksillustrated.com/images/document/howto/SO96_HTbeef.pdf

You might also like to try using it for Chicaco Italian beef sandwiches.