You could try making yourself more of an oddity than a terrorizer. I worked in a haunted house at an amusement park, and I was having this same discussion with one of the haunt actors who worked in the line. She was also constantly exposed, and needed to entertain without necessarily being able to sneak up on any of the patrons. Here are some of the ideas we tossed back and forth.
1. Be a bashful or flirtatious monster-- think overdramatic and cartoonish. This will encourage people to approach you. Say something ridiculous or creepy to them (if you are in a particularly themed area you can think several related conversation pieces)This may not get people running and screaming, but you will be memorable.
2. Instead of going for creepy/possessed, just try a little unbalanced. Pick imaginary bugs out of your hair (or your fellow actors) and pretend to eat them. Approach stationary people and stare blankly/affect a tick. Stop suddenly and shriek (The actor I was speaking of previously would rapidly blink just one eye and then scream and abruptly stop). Start clawing/pulling at your face and scream "Get it off! Get it off!"
3. Get creative with hiding places. If you are out in the open, but there are bushes, garbage cans, food stands, etc. to hide behind take advantage of those for a jump and scare. As a tip-- a good, low "growl-y" sort of scream or roar coming from a woman tends to make people a little more likely to trip over their own feet, in my limited experience. Of course it's also more likely to irritate your throat, so choose wisely
Obviously props can be fun and helpful as well, but can be hard to get them approved. If you can get your hands on something it opens up all kinds of options.
I'll brainstorm and see if I can come up with anything else, but I hope these are at least moderately helpful for you.