I hunted public land a lot up until a few years ago, when I got a promotion and could afford to join a lease for the first time.
To kill deer more reliably, I had several tactics that helped me out a lot.
1 - Find some heavy cover (large thickets, swamps, etc) and look for trails near there. Don't hunt those at the very beginning of the season, but move in that direction as you start seeing more hunter pressure in your area (or if you stop seeing deer). Once you've hunted those areas some, sightings will fall off, so consider that your "Ace in the pocket" and don't play it until you need to. EXCEPTION - if hunting a WMA that gets heavy hunter pressure all the time, I exclusively hunt areas in the WMA that have heavy cover and small openings, because no one else wants to hunt there. Be creative about how to create opportunities. For example, a few years ago I hunted in a place with no climbable trees and heavy waist-high ground cover. I cut the top out of a bush, and used it as a "Standing blind", and just stood behind/inside the bush with a shooting stick. I killed a deer with a pistol like that, and another with a rifle.
2 - if you don't own a muzzleloader, get one. My success during muzzleloader season is substantially higher on public land than modern gun season. Be sure to clean the gun well after practicing, and do your best to hunt some weekdays during that time early in the season. The deer are largely unpressured at this point, which is probably *more important than any other factor* on heavily/moderately hunted public land. All the trails, sign, food, and awesome vantage points you have might be worthless if the deer have been driven nocturnal. My reality in deer season was that I killed all of my deer by the end of the first week of gun season. After that, my sightings plummeted.
3 - if you are hunting a WMA along a lake or river, use a boat to hit property that isn't accessed commonly by others. One of the easiest muzzleloader hunts I've ever been on was on the banks of a lake on public land. My buddy and I hunted maybe 100-150 yards off the bank of the lake. I shot a big doe, and it was a quick drag to the boat and the work was done. In some areas, a $300 used jon boat with a trolling motor will get the job done.
4 - Note where other hunters access the property, and think of ways to do it differently. A great example would be getting a bike and riding down the road away from the parking area, then chaining the bike to a tree in a spot where vehicles cannot pull over (keep it hidden!) and go in from there.
Notice a trend to my advice? I spend very little time looking for deer sign until I can find a spot that I'm not sharing on a regular basis. I've seen deer forsake prime-LOOKING spots and hang out in areas that made you question their sanity, all because hunting pressure pushed them there. If you can't find an area where deer are moving around semi-comfortably in the daytime, then your odds are usually low. Also, try to keep at least one spot (possibly the farthest one away, or hardest to access) in reserve for the peak rut action time in your area, and then make the trek in for an all-day sit (or at least until after lunch). Mid-day movement of mature bucks is a common phenomenon during the chasing phase of the rut.