There's really just so much that you can do to deal with having props of an unwieldy size, most of it being pre-planning.
Know your venue so you don't get caught in small, high traffic areas. Plan photoshoots in open or outside areas. Create harnesses/holsters when possible. Have a friend to act as a handler. Plan ahead for times you may need elevator access. ect.
Make sure you know, and abide by, your con's size/weight/material restrictions on props as well. Larger items are magnets for attention, but they're also magnets for scrutiny. That said, if you know you're in the right, don't be afraid to point it out. Keep a copy of the policy on you, pulled up on a smart phone, ect to back up your claims.
Another option to actually creating these massive, difficult to manage props that I've seen get positive reception is to make a super deformed or plushie version of the prop. Aside from scaling down the prop to a smaller size, you really just have to suck it up and deal with the negative aspects of carrying around a behemoth.