I routinely fish a lake that has a lot of standing timber. Let me offer a couple of options for you to try.
To start with, I'm assuming you've got a boat and aren't shore bound. First, structure ( as opposed to cover) is still important. How would you fish this lake if all the trees and such weren't there? There are still points, ditches, high & low spots, etc. There is still probably still a weed line. This is where I'd start. Now, trees and submerged & partially submerged bushes and such add value to those spots.
Don't start by fishing every tree on the lake. Fish the trees on the points first. Fish the trees on the points that are getting the most wind that day. Fish the shady side of trees or bushes on points that are getting the most wind that day. The old Buck Perry slogan still applies, i.e. "The fish are deep - or shallow - or somewhere in-between."
You didn't have any luck keeping your wacky rigged senko from getting hung up. Thats probably my favorite tree fishing bait. Did you use a weedless hook? I like Falcon weighted weedless hooks, (1/16 oz), but any of the weedless spring style hooks will work. You really need a foot or two of visibility ( and more is better) for the wacky senko to work. At least, that's what I think. For me, senko is a confidence bait and I lose some confidence when the water is very stained or muddy.
Anyway, a wacky senko drifted down on the shady side of trees, on points that are getting the most wind that day, is where I'd start first.
You might want to take a more active approach - looking for a reaction bite, try throwing cranks. Just my opinion, but I think that the best crank for cranking timber is a Timber Tiger. You can get them in all different depth ranges. Me, I can get a DC16, which is supposed to get 16 feet down on 10 lb line, on an abrasive resistant 14 lb line, I can get down an honest 10 feet or so. You will be amazed at the kind of brush and cover that bait will come through and not get hung up. You will get hung up from time to time so invest in a good extension pole type retriever and also one of those hound dog style of lure retriever.
A jig can be a good tree lure. A tx rigged worm can be a good tree lure. A tube can be a good tree lure. I generally fish trees using 14 or 17 or 20 lb fluorocarbon line - just depends what you think you can get away with. You try to determine where in the trees the fish are hanging at. They can hang out on the edges of the submerged branches, or next to major linbs or next to the trunk you never know, trial and error throughout the day until you put together the puzzle for the day.
Find out what the forage base of the lake is. If you can find a sharply sloping clay bank, you've probably found a spot where lots of craw dads live, might be a good spot to put some time into. Somewhere on that lake there are different kinds of cuts, indentations, coves, whatever. Areas where deep water is kinda close to shallow water can be prime areas.
There is no substitute for time on the water, but I hope this rant offers some ideas and areas on where to start.