Shaking upon acceleration and higher speeds

INFO: 1993 Honda Accord with 175,000 miles.
My car starts to vibrate/shake when accelerating over 50 mph, and at about 65 mph it shakes continually. However, it's perfectly fine when driving UNDER these speeds. The steering wheel shimmies slightly, but it's more of an "up and down" vibrating. We have taken this car to several shops, including a Honda dealer, but nobody has been able to figure it out. We have had bent wheels replaced, new front end parts all replaced and front end alignments done, brakes done (including rotors), new tires and still it shakes. My husband is now thinking it is the struts, which are original, even though all the shops have said they are "good". Any ideas out there? I'm going on a 5-hour trip next week and would love to have this fixed before then!
Thanks in advance,
Linda