Yes, you will need another visa to enter tanzania, and if I where you I would fly there :-)
The only way is to fly ( save time if a short break ).
Otherwise as suggested , by road to Dar-es-salaam and then ferry to Zanzibar.
Fly 540 have some good offers for flights to Zanzibar from Mombasa.
Alternatively , there is Precision Air or Kenya Airways.
As for the the tour companies , log on to www.katokenya.org
Hope this helps.
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