We did a liveaboard in Belize followed by a stay inland near San Ignacio to do jungle stuff. We did a day trip to Tikal from there, which was good and we saw plenty for us, but it was a long day. You can also stay by Tikal if you want more time there, or some time early/late in the day when there's less people and it's cooler, but I have no first hand experience. There are lots of tour companies that will arrange various sorts of tours and stays, and the lodges will also arrange things. You could probably arrange a stay at a lodge in Belize and arrange to leave gear there while you did an overnight or more at Tikal then came back.
I'm thinking if you want to see Tikal specifically it would best be combined with a Belize trip, as I'm not sure there is any convenient way to get from Roatan to Tikal, but I could be wrong. If you're not set on Tikal you could also look into seeing Copan in Honduras, if you flew through San Pedro Sula.