The fixed price per item is a swings and roundabouts quoting method.
It takes the risk out for the client (You have a fixed cost) - and it makes less hassles fighting over who took how long to do such and such
The saprky might loose some money (time) if he hits an issue, or he might gain if it goes better than expected.
Get those other quotes - t&m by and after hours job is the best way for that size project.