Is there an effective scanning strategy that avoids the Reapers?

This strategy lets you avoid reapers while still giving you lots of time to get your scans done.

Enter into the system you want to scan, scan twice wherever you want to (I try to be systematic but it's up to you). On your third scan the Reapers will appear, so it's helpful to be near the edge of the system. Before you hit that third scan, look at where you would like to reappear (top, bottom, left, right). Scan and move out of the edge of the system bringing up the galaxy map. If you're reasonably good at avoiding Repears you can probably get a few extra scans in before leaving the system.

Remaining inside the ring, point your ship in the direction you want to re-enter the system. For example to show up next to the Mass Relay you would point your ship right.

You will re-enter far enough away from the reapers to perform more scanning. Repeat this technique until you've completed your scanning. Note that the reapers don't move closer to you while you are examining a planet/etc so you do have time to land and get your probes launched.

This video demonstrates the technique effectively.

Enter a system, an autosave is made, scan as much of it as possible until the Reapers catch you, be caught, click Resume - you will start in the same star system with no Reaper awareness, scan what you found and get out.