I have waaaay more experience with this than I care to. Two separate F350s. Unfortunately you cannot simply replace worn parts when you find them and not do the entire steering system. I tried that. Chased the death wobble in both trucks for upwards of a year each. I would inspect along with the help of very knowledgeable coworkers, find the parts that are visibly worn, and replace them. Well at that point, other parts designed to wear and fail are on their way out. Not sure if you have experience working on your own vehicles or have any knowledgable help, but here’s what I would do and what finally fixed it:
Replace the following with parts that you get directly from Ford (NOT “OEM” parts from an auto parts store): Track bar, tie rod ends, and drag link. These all have bearings that I would bet you can see movement in. Upgrade the steering stabilizer. I would place big money on this thing being shot. DO NOT put an OEM stabilizer back on. I have had them come off the shelf bad or only last one decent sized pot hole before giving it up. Rancho is not an upgrade; I tried a Rancho stabilizer and it did not help. I put a Bilstein stabilizer on mine, along with the other replaced parts, solved my problem.
Other possibilities to look at are hub bearings and ball joints. These are less likely to wear as rapidly, but the first death wobble truck I dealt with, they were worn and needed replacing. The second truck, they do not have play so I have not done them.
Here’s an easy way to check for worn parts (aside from the obvious like shreds of elastomeric bearing hanging from the component ends): have someone turn the truck on, leave in park (with break set if it makes you feel better), crawl underneath and look at all the steering components as your helper turns the steering wheel back and forth. As the wheels turn, you will be able to see play in the bad joints. All the ends should be very tight and you should not see movement in the various bearings.
Here is the reasoning behind only Ford parts (aside from the stabilizer; I cannot stress this enough). Two years ago my truck left me stranded in Tulsa after a horse show, with a horse and great need to get home and back to work. I took the truck to a shop and explained what all I had replaced and desperately questioned why I keep having death wobble despite all the parts I had thrown at it. The manager explained to me that the specs on various manufactured parts are copyrighted. While other manufacturers advertise their parts as OEM, and the specs are super close, the measurements are off by just a smidge. I wasn’t so sure I believed him but was going to explore this on my own.
Fast forward a week or so, I limped that thing home about 700 miles with the wobble still there, because they had replaced what they “found” to be bad; as I said up thread, other parts have endured the wobble and are degrading by this point, even if you cannot see the wear. I bought a Moog track bar from the local auto parts store, and a Ford track bar from the dealership. Both brand new, out of the box, I took measurements of the inside diameter of the attachment bolt hole. I don’t remember the difference, it was a very small number, but it was enough to make a difference. In the scheme of what steering components do, any little bit of slop in the attachment fittings will cause death wobble.
That is when I threw all the parts at it that I bought at the Ford dealership, and a new off the shelf stabilizer because it was going to be a week or so for my upgraded stabilizer to come in. The steering felt tighter and otherwise great… until I hit a certain bridge joint in town that is particularly bad. Death wobbled twice on that bridge. I put the Bilstein stabilizer on and haven’t had an issue since.
So, long story long. Use only Ford parts, replace ALL of the steering components at once, and upgrade to a better aftermarket stabilizer (highly suggest Bilstein). I don’t know what this all would cost to have the dealership do, I also don’t remember how much it cost last time I did so. But it was under $1000 to do myself. The job is not for the faint of heart. The track bar bolts have a tendency to seize in and often have to be torched/cut off. When doing reinstall, do not skimp on the anti-seize. It seems like a massive undertaking the first time you do it, but with the right tools, this all can be done in an afternoon.
Not sure if any of this is in your wheelhouse, but perhaps it can help someone down the road (pun intended). I’ve had this happen both loaded and unloaded. It is a problem, certainly a weak area in Fords (thought can happen in any vehicle). Lots of people have issues with it and never solve it. But perhaps they never get to the bottom of it because they only replace a component or two at a time. Holler if you have more questions. I have lots of premature grey hairs from this…