The online maps I use don't identify Soldier Lake, but I am assuming they are the lakes just south and west of "The Major General".
Here's a link to the Gmap4 map
of the area. On the map, satellite view, you can see there is a well-constructed zig-zag trail heading east out of the Soldier Lake area. That must be the trail you saw last year. It is not marked on any of the maps that Gmap4 accesses.
I think the reason most people go S out of Soldier Lake is because there is a trail heading that way. If you follow that unmarked trail and head up the drainage above Soldier Lake, you will need to gain 300-400' extra feet of elevation and then lose it dropping down to OAP.
If you take your proposed route, the map link is set on satellite view to show the point( in the cross hairs in the center) where I would leave the trail and head SE toward OAP. You would still need to climb up and over the ridge to the south.
Have fun, whichever way you go!