Take a page from The Lion King and Avenue Q
For the lion King:
They have puppets controlled by actors dressed to match he pattern on the coats. Instead of going for a Beauty and the Beast level of theatrical similarity, the showing of puppets-as-puppets allows audience members to choose to suspend their disbelief without needing to convince them that rubber-forehead aliens are lions.
For avenue Q, the actors playing the Monsters all wore pure black, though again with slight style changes that evoked their characters:
For a larp, a puppet of the creature you're impersonating can do the same thing. Make sure that you capture its face and arms, and use the arms to give it the necessary sense of size. If you suggest details through lightweight components (ala lion king) instead of trying to render the entire monster, you can allow people to interact with it without needing to spend the time to model the whole thing.
In terms of giving a large size impression, simply model its features on an appropriate scale, and insure that the bounding features are all present. Arms, legs, and shoulders&head should be sufficient to give it a sense of size. By strapping its legs to your shoes, offset by divots, you can simulate its baseline stance and shoulder width. By having its arms on poles, you can simulate its reach, And by giving it a head, you give players something to make eye contact with instead of you.