It's very very simple:
There needs to be an active "brokerage" or hook-up system run by the Wildlife Department free of charge (or even for a small fee to one party or the other) that hooks up landowners with licensed hunters. The landowners can charge whatever they want, from $0 on up, but will be encouraged to charge $0 or a minimal amount.
The problem is landowners charging too much. If they want the population curbed, then they need to lower their prices dramatically for honest hunters who are ready, willing, and able to take out the piggies.
Don't want so many pigs? Quit charging so danged much. Not rocket science. Charge a small fee for a "pig season only lease" that runs from Jan 16th to Sept 30th, so that there's no way they can be in possession of a deer carcass legally or tag one. Etc.
Thats a great idea for landowners and seems like it could easily be accomplished by the ODWC with a little effort. Even still, theres a festering problem with hogs on public lands that aren't very accesible and its growing pretty fast. As long as the hogs aren't kept in check on public lands private landowners are going to continue to have problems with them.