Wendell - I have had a similar problem with the inboard doors on my 360.
Now's a good time to give a report as I believe that I've finally solved the
problem.

Since nearly day one (three years ago) I've had a noise and vibration at
higher airspeeds.  It took awhile to determine that it was gear door related.
Along the way Lancair and I guessed that the plane actually had two noise
sources, based on the differing airspeeds where it would occur.  About 4
months ago I noticed some gouging in the pilot's side of the nose gear well
where the screws attaching the tire guide to the strut assembly were obviously
hitting.  On jacks, I determined that there was enough side to side play at
the wheel to explain the contact.  I eliminated the side play at the strut
attach to the engine mount and relieved some wheel well material at the
contact point.  There is no clean way to adjust the side to side position of
the gear so you have to get it right during build.  That took care of the high
speed vibration I would sometimes encounter at the top of the green arc.  I
say sometimes, because clearly, the wheel to well contact would depend on what
angle the wheel was at when retracting (I don't have the self centering strut
and Vern told me to expect an $800 price to have Lancair do the conversion.)

During the next test flight I noticed that another vibration and noise was
still present.  It was a bit less severe now.  I still knew it was gear
related because when I cracked the cross over valve, I could eliminate the
noise.  After a number of incorrect guesses and door removal experiments, I
finally removed the interior so that I could feel around to locate the source.
Sure enough, the right inboard door was humming away in the upper third of the
green arc.  I could see through the side panel cutout for the hydraulic
cylinder.  The door hydraulic cylinder was vibrating and the attaching arm to
the door was really humming.  The Lancair guys suggested three fixes:  replace
the door hinge, increase the pressure switch setting, or increase the door
load by shortening the up stop.  I went after the hinge first because it
seemed to short and the bracket attachment pad to the door did not seem stiff
enough (a lot of door flex under load).  The hinge was deforming at the front.
The upshot is that with door stiffening and a longer hinge (the hinge extends
forward of the cylinder attach point) the vibration is gone.  I did not adjust
the hydraulics.

One lesson out of all this:  don't guess at what to fix, determine the cause
first.  I never could figure it out until now and consequently have four gear
doors that have to be cleaned up (a lot of refitting occurred) and repainted.
In your case Wendell, assuming you are sure you know which door it is, look at
the shape of the door retracted on jacks and look for deformation.  If you can
put your hand on the retracting bracket during flight, that may give you a
sense of whether it is the hinge that is the problem (the bracket vibrates
differently than if the hinge were solid and the door were opening and closing
further outboard)  If there's no vibration and the door's just getting sucked
open at the rear due to localized low air pressure, you might try re-shaping
the door to add pressure against the rear flange.

Hopefully this will help.

Ed de Chazal
361DC