I'm not sure if it is the same, but I've had something like this ever since I got the rig. I never drove over 55 during the test drive (with tires that had good tread but were six years old), and then right away I got new tires (Michelin LTX M/S2). At any rate, I then did get a chance to drive faster and immediately noticed a sort of "judder" that became noticeable at around 60 mph, and got worse between 60-70.
It seemed like it was in the front end, but I was never sure. I could definitely feel it in the steering wheel, but then also I could feel it in the seat, and I could see things like the passenger seat back (when unoccupied) shaking in time to the "beat." Ugh! It does not change if I put the rig in neutral at speed, nor does braking affect it. I think it might reduce somewhat over 75mph, but then I don't drive that fast on a regular basis.
I have done a number of things that
haven't yet fixed it, so I'm still not sure what it is. I do, however, know more about what it isn't

Maybe the same as yours? Here is what I have done. Most of these things were for other reasons or as a part of other jobs, but in my mind was always "will this fix the shake?"
0) Got six new tires just at the time of buying rig. "Found" shake upon driving home (first time over 55 mph).
1) Got four new shocks, Koni FSD. Also had wheel bearings re-packed, brake caliper slides lubed, etc. Plus general check-over and other unrelated maintenance. Nice improvement in handling, but no change in shake.
2) Had all six tires and wheels removed, dis-mounted/re-mounted/re-balanced as a part of having extended (Tireman) stems installed. Found one bent rim on rear and replaced it with used/better rim; also found out that spare rim was bent (so did not swap it in), and that front left rim was very slightly bent (also found out that this is quite common with Ford steel rims. Maybe it's more accurate to say they are "untrue" rather than "bent," as it's not like something caused by a hit or etc). Shake still there, so front/left rim was on my mind for next possible culprit.
3) Had drive shaft out as a part of beefing up transmission (because it was removed in order to remove transmission). No change when it was put back (not that I expected any).
4) Had entire new front end put in from 2014 van. The main reason was for the super-beefy brakes, but since all of the front end (except for springs, wheels, and tires) is new, I can pretty much eliminate any of those components. Also put on beefier front anti-sway bar, plus beefy rear anti-sway bar, not that I expected that to affect the shake. Had run-of-the-mill alignment done (this is necessary with new front end regardless). Shake lives!
5) Had left front wheel and tire removed and checked at shop with Hunter Road Force balancer. The fact that the rim is slightly untrue was verified, but with the Road Force balancing the tire and wheel as a unit were brought to well within spec for overall balance/shape. Shake still there!
6) At the same time as #5, I added a small steering stabilizer* (Safe-T-Plus), and changed the rear to a milder anti-sway bar and slightly softer (but adjustable) shocks (for better ride). Also had super pro alignment done (Henderson's Line-Up - they are specialists). No change in shake. Now this is getting annoying!
7)....? I haven't really decided what my next move is. Possibilities:
a) I did buy two new (reconditioned) Ford steel rims (which are supposed to be truly true) and may have those put on along with two new front tires (not that the front tires are done for yet, as they only have around 15,000 miles on them, but the spare is ancient, so I could take the best of the two existing front tires and make it the spare, plus have two BRAND NEW front tires AND rims, both Hunter Road Force balanced, which should eliminate that from the equation (plus make the spare more viable).
b) On the other hand, maybe four Alcoa aluminum rims? They are supposed to be super true, although there are a few negatives: One is they are expensive and I don't have any problem with the looks of the simulators; two is that the extended valve stems don't mate perfectly with them (I'd have to have them bored out slightly); and three is that I'd still have two steel rims anyway (inner rears).
c) Or maybe it's time to see a driveline specialist. I'm beginning to suspect it is either driveline related or perhaps something bent in the way of a rear hub? I do feel the shake in the wheel, but then I'm not sure that means it is in the front end, since I can also see "general shakery" in the intererior, and I have a new front end.
I'll probably do a) or c) or a combination thereof, but haven't decided for sure yet. I guess to look at the bright side, I'm not likely to get a speeding ticket
BG
* Reason I say "small steering stabilizer" is that when I had the complete rig evaluated at Henderson's, they said it really didn't have any major faults, so nothing was really "necessary." Still, I like a super crisp handling rig, and I had found that the new, super-beefy rear anti-sway bar caused the rear to be too harsh ("hopping" over bumps that I wouldn't even notice before). But I liked the good handling! Ultimately I went with a medium sized rear anti-sway bar (there is none in stock configuration) and slightly softer/adjustable Koni shocks on the rear. Then I tried the recommended size steering stabilizer on the front. Well it was just overkill. Yes, it did make the rig feel like it was on rails on a straight stretch of freeway, but driving on a twisty highway was torture (too hard to steer) and it was similar just driving around town (turns). So I went with a smaller stabilizer of the same brand - one that was meant for a Toyota Dolphin, I believe. I would actually like one just between the two, but they don't currently make that size (however they may in future).