Can a sacrifice be used to pay for more than one effect?
You're absolutely correct: you can only sacrifice the Mogg Fanatic to pay the cost for one of those two effects, not both.  From the Comprehensive Rules:


  117.10. Each payment of a cost applies to only one spell, ability, or effect. For example, a player can't sacrifice just one creature to
  activate the activated abilities of two permanents that each require
  sacrificing a creature as a cost. Also, the resolution of a spell or
  ability doesn't pay another spell or ability's cost, even if part of
  its effect is doing the same thing the other cost asks for.