The backfire helix antenna is quite easy to build, cost near nothing and definitively solve this position error problem.
Various helix antennas can be found, i used this one as a guide : http://lea.hamradio.si/~s53mv/navsats/analog.html
Most GPS provides power through the antenna connector, in this case i had to add a 18pF capacitor for DC blocking purposes and avoid a short circuit with the new antenna.
A classic ceramic capacitor can be mounted on top antenna. Value is not critical, just select one from 10pF to 47pF.
I also did the same modification with a M8N module that has a built in magnetometer.
Another example using a SMA connector, the DC blocking capacitor is soldered between the antenna pin and SMA connector, close to the GPS module on other pcb side.