VPI Prime Sig/Lyra Delos / Feedback ...help!

I have heard a number of uni-pivot arms, including two that I owned (Graham 2.2t and Basis Vector 3) and none of them suffered from any feedback issues.  These arms were used with Lyra Helikon and Titan cartridges.  If there is a feedback issue (resonance) it is either a very unfortunate combination of all of the mechanical parts of your system--the cartridge, arm, table, table support--or, a defective cartridge.  

What you are calling feedback when playing loud passages might be mis-tracking.  That mis-tracking can be a product of incorrect alignment/setup or, again, a defective cartridge.  

It is almost assuredly not an issue of incompatibility with your phono stage.  The only kind of incompatibility that would remotely sound like feedback would be an overload (too strong a signal being fed into the phono stage), but, that is not the case because you heard the same problem with different gain settings.  

My "bet" would be mis-tracking caused by a defective cartridge.

The Lyra cartridge is NOT prone to resonating and causing feedback problems.  It is most likely the combination of the arm/cartridge/table suspension that is unfortunately tuned to a resonant frequency that is causing the feedback.  You could try adding a small amount of weight to the headshell to see if it moves the resonance to a less sensitive frequency, or you can try tuning the table to change its resonant behavior (put it on a different platform, add weights to the plinth, etc.  

It probably makes sense to reduce the overall tendency of the platform the table is sitting on shake--if it is on a rack, can you make the rack more rigid?  If the rack is close to the wall, the best way to make it more rigid is to somehow attach it to the wall.  I did this by putting a cleat on the wall near the top of the rack and then using angle braces to attach the rack to the cleat.  This made the stand MUCH more rigid.

Mijostin's comments make sense.  If the arm is already too heavy (meant for a low compliance cartridge) there is nothing much that can help.  You have a basic incompatibility, and perhaps a beef with the dealer who sold you the cartridge.  It is not the fault of the cartridge--it is like putting the wrong kind of tires on a car and blaming either the car maker or the tire maker for the poor performance.

While you might not be able to cure the problems that result from this incompatibility, you might be able to reduce the feedback by changing the isolation and tuning of the table's suspension (try different platforms, different feet, try making the platform the table is sitting on more rigid, etc. If your unipivot has provisions for damping its motion you can change the amount of damping.  

Are having any footfall problems as well (do you have to tiptoe around your phono setup when it is playing to avoid skipping?).  It is common to have footfall problems with suspended wooden floors and this can complicate the solution because solutions that reduce your feedback problem may worsen any footfall problems.  With a wooden floor, it is probably best to put the table on a wall mounted turntable shelf--that would reduce feedback that is coming from the floor (your floor is like a giant sounding board picking up vibrations from the air as well as from the speaker cabinet that is grounded to the floor) as well as any footfall problems.  As I mentioned before, you can also work to make any rack your table sits on less prone to shaking (attach it securely to the wall).  After you have a solid foundation for your table, you should then try various shelves and platforms designed to damp vibrations.  It is hard to say which will work best as this is a matter of system- specific tuning.