First, I don't think anyone is served well by the ambiguity of the legality of corner crossing. I think the best place to start is to define clearly if corner crossing is legal. If if is, under what conditions (i.e. does there need to be a pin/monument, what about fences that exist, etc.). I hope that the Wyoming case discussed by the attorneys in the second podcast will be a step on the road to better defining this -- thus, my meager contribution to the cause.
Second, what seems to be missing from much of the discussion here is the degree to which recreation in general and hunting specifically has becoming a highly valued commodity in the past couple of decades. Thus, an outfitter can charge $9000 for an elk hunt not just because they have a lot of area to hunt but specifically because they can keep others from hunting it. I don't see them giving up on this easily. If corner crossing becomes legal, I think that you will see a spike in the number of land swaps to segregate public from private so that they can maintain their exclusivity -- in my view, the exclusivity is more important to them than the acreage.
If it ends up that corner crossing is deemed illegal, then I think you have to proceed along much the same lines as we do now: trying to secure access agreements, walk-in areas, etc. But I would also like to see an increased push for land swaps first and land sales after that. I see no value in a public parcel that can't be legally accessed and is only producing a value equal to the grazing fee. Why not let these truly landlocked parcels be bought and create a permanent trust with that money to purchase other parcels/access in the future. You could also grant the public the right to pursue legal access under the same statutes that a private citizen might (this would work for Wyoming but probably not any US gov't lands) -- it would be costly, but might be worth it in some cases (e.g. maybe a 1/4 mile easement would open up 3,000 acres of public access, like would be the case for Squaw Mountain west of Wheatland). But for this you would have to have a budget for it and an agency group prioritizing the use of the budget.