this is a good question I would like to see the answers you receive?

Paver edging is necessary in these situations to maintain/reinforce the line. Just google it as there 20 gazzillion types out there.

http://www.homedepot.com/p/ProFlex-ProFlex-6-ft-Paver-Edging-in-Black-1260-HD/203706944

Paver edging will fix your problem. No concrete required.

paver edging is only a solution IF the original installers extended the compacted gravel base far enough past the edges of the walk to accommodate it. Just spiking edging into soil will accomplish somewhere between diddly and squat. Can you confirm if the base comes out far enough?

am I seeing what I think I'm seeing - did they notch out a paver for a sprinkler head???

Adding the wooden stakes is a good idea -- should help stop the "creep" if you compacted gravel base isn't an option.