HI!
Bottom round roast I do on the   NG grill, pretty much similar with a smoke box.
What I do is this :
Take out meat,  I use a tenderizer to open up the meat . oil up the roast with evo, and season as desired, I use salt pepper garlic onion oregano. Adjust to yur liking. Return roast to the fridge for an hour or 2, or overnight .  Grilling as follows:
Similar to smoking go very low,225 to 250 max!
Adding liquid : I use apple juice/cider.  It gives moisture, flavors the meat, breaks down the protein .
Either rack the roast and add liquid underneath or use a separate pan ?
Once set up? I do not open the grill for 1 to 2 hours>
Check the roast ?  flip it over if it cooking too fast.  sprite it with liquid
Adding liquid, add water, more apple juice is too much acid !
Cooking time ?  Depends on the cook temp ?
I usually pull my roast @ 140/145 max.
Let it sit and fire up the grill to do Baked potatoes.
If you want a crust, can do a reverse sear?  I find its not needed?
Like  MR  beef.
Just remember not to use high heat in any form in the beginning, it will toughen the meat !
I do this almost monthly, even in the oven.
Sorry for the lengthy. 
Go Slow and Low, Add Juice