In theory, yes.  In practice, no.
That well nut has thousands of hours on it and I keep it properly lubed.  Since the threads in the well nut are brass (rod and other nut are steel) they will be the first to go.   I just pulled the well nut off and the threads look great.  I would guess the rest of that printer will be in the garbage before I wear out any of the threads.  Even if the threads begin to wear (which is inevitable) simply tightening the well nut will solve the problem.  When the well-nut fails I will have no problem spending another couple bucks to replace it. 
Is this the most precise solution? NO
Is this a simple cost effective solution? YES

I wasn't referring to the well nut wearing off.  I was referring to the wear he (mwille) would put on the screw & nut, if he were to tilt the nut by shimming it on one side, as he's proposing on post #15 above.

I'm not sure that is doing what I was thinking about.  I thought what you pictured uses compression/pressure to keep the load on a single side of a thread face on 2 different nuts.

Here's a picture of my Press Z screw/nut (grease and all).  I was talking about simply loosening the 4 screws that hold the brass nut and adding a thin washer under one of them so it would tilt it when tightened back down.  This way a single nut would have contact with both an upper & lower thread face like the cross section shown in the 2nd picture below.

Could you clarify whether or not that is a metric rod? Considering it's built in china I see no reason to suspect it is imperial - is that an M5 rod?

I'm not sure that is doing what I was thinking about.  I thought what you pictured uses compression/pressure to keep the load on a single side of a thread face on 2 different nuts.

Actually, in that setup, you have 2 screws, one built into the bed, the other into the well nut.  The compression in the rubber wants to push the 2 nuts in opposite directions, So the bed nut presses downward into the upper surface of rod threads, the well nut, pushes upward into the lower surface of the rod threads. This is how most anti-backlash nuts work, except they use a spring between the 2 nut sections.

The springiness of the rubber (or the spring), prevent undue wear on the parts, yet take up the slop.

Something like what you're suggesting might work for a period of time, but it will eventually wear out ends of the threads on both the nut and the screw to the point of becoming sloppy.

There's software solutions via firmware available though.. Search the site for some..  But by standard it's a very niche issues specific to the solidoodle and it's mechanical construction

Here's a picture of my Press Z screw/nut (grease and all).  I was talking about simply loosening the 4 screws that hold the brass nut and adding a thin washer under one of them so it would tilt it when tightened back down.  This way a single nut would have contact with both an upper & lower thread face like the cross section shown in the 2nd picture below.

It seems to me that Z-backlash on the Press opens up a whole new can of worms with its "standard issue" non-level bed.  Due to that slope, wouldn't it effectively apply the Z-backlash problem to changes in Y movement as well? 

So anyway, I was wondering, has anyone ever tried to fix backlash by simply shimming the z-nut on one side just enough so that one side is in contact with the upper thread face & the other contacts the lower?  It seems to me that it would accomplish the same thing as an anti-backlash nut (as long as it wasn't shimmed so much it tried to tilt/bend the rod & put it in a bind). 

A side effect would be that it should reduce friction since it wouldn't be contacting the entire thread faces.  The down side to that is that it would also wear those points of contact more quickly.  The question is, how quickly would it wear down to the point it allowed backlash again?

but my question is do you think it would make much difference?