One approach you can try is to first turn your polygon features into line features using the Feature To Line tool. Important: the "Output has M values" geoprocessing environment setting should be set to "Enabled" so that your output lines can store M-values.
Turn the lines into routes using the Create Routes tool. The objectId of the lines will be your route id. Your measure source will be LENGTH. This will update the M-values on your lines to the length along the line.
Now you can place point events along these lines using the Make Route Event Layer tool. You'll need to create a table of the events. An event would be a route id and a measure (say 10 meters) along the route. The result is a point exactly 10 meters along the line. You can offset the point to the left or right of the line (inside or outside the polygon). The problem with this is that you have to construct the table of events, something like:
RouteID, Measure
1 , 10
1 , 20
1 , 30
2 , 10
2 , 20
etc...
If all you need is a graphic display, add the output of Create Routes to ArcMap, right-click to get properties, and there's a tab for Routes. You can place symbols along each route line at defined increments. I don't know how to export these symbols to features however.
There's probably an easier way, but the Feature To Line -> Create Routes will at least get you M values that you can experiment with.
