I've never had a computer that auto-offs after so short a time. My Planet Bike is at least 5 minutes. No idea on how well it would perform at very low speeds.

One thing you could try is to mount two or more magnets and do whatever creative thing you need to in order to make it work right. Since your circumference should be 958mm, maybe mount 3 magnets, giving a pulse every 319mm, and enter 3190 as your circumference? Then you could just divide everything by 10, and you should get perfectly adequate responses on everything since you'll be getting more frequent pulses on the sensor.