Some things that cause the syptoms (in front wheel drive vehicles),you speak of are;
worn twisted or bent axle shafts (there are two)
Loose or worn wheel bearings
warped or damaged brake roters or drums (front or back)
loose or damaged motor mounts. (especialy the upper mount)
Engine problems (as
Mark 18 mentioned).
Rear wheel alignment balance and or damage. (to include rear shocks)
Improper tire preasure.
I noticed that you have already iliminated the possibility of some of these.
Take it to garages that will take it on a test drive with you driving or present. Go with them and point out what your talking about.
Get a commited diagnosis of the problem before spending any more money on repairs. Get a estimate with warrenty or guarentee of the repair fixing the problem.
Notice the behaviour of the problem. So you can best explain it. Know when it does it and how to make it happen, so you can show it.
Take note of when and where it shakes /vibrates the worst or when it doesn't have the symptom.
Note if it does it when accelarating, driving at certian speeds, when slowing down or braking ,when driving straight or in curves, Up hill or down hill, on dry roads or wet?
Does it shake or vibrate the whole car or just the steering wheel?
Be prepare to ask and answer questions.
Hondas like most other cars are unibody(that means it doesn't have a frame as such) The frame is an intrical part of the body structure. Though extreemly rare, if the vehicle has been in an extensive damage accident or severely rusted the unibody structure can be weak and or damaged causing the mentioned symptoms. But there are other symtoms or signs of this which accompany the symptom if this is the case.
Doors that don't latch or open properly, misalignment of hood, hatch back or doors. Excessive rust including holes in the body, floor board or undercarage.
Some times older cars with high millage will develope a drive line wabble or shake that is just isnt practicle from a cost perspective to iliminate. A combination of engine and drive line wear can cause this.
Perhaps you are like myself ,where noses shakes or unusual wabbles or querks bother you more than the average person. Because of my nature and sensitivity to such things ,(being a mechanic for over 30 years), I often notice and sometimes get anoyed with such things when others don't even notice them.
BTW/FYI search the internet for Honda forums. These forums and people my be able to help.
Sincerely
Cliff