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Being that it is an '05 perhaps your Mag Ride Shocks are leaking and shot -
Have you checked them for leaks or to see if the shipping blocks were removed (probably were)?
Have you checked to see if you have MRC shocks or if the previous owner (unless you are the OG owner) removed them, disabled the system, in favor for other aftermarket shocks thus making your ride quality suffer?
On the flip side there are multiple options for you to disable the F55 suspension on your 2005 (either with simulators or turn it off with a Tech 2) and replace the MRC shocks with aftermarket shocks of your choice:
Shocks
Coil Overs (more involved than just slapping these on)
Z06 Shocks
Koni FSD or another Koni selection
C6 Z51 Shocks
Bilstein shocks
Etc.
Sway Bars
C6 Z51 or Z06 (do your research first on installing the Z06 on a base Vette first)
Hotchkis
LG
AFE
Etc. - but there are many to choose from, so some research is needed
However, it will be helpful for you to respond back here with some more input and information in order for us to assist further -
My 2009 MRC suspension was great but I put on C6 Z51 sway bars (made a huge difference) and did the 2009+ up Jim Mero MRC Suspension Reprogram and it really made a huge difference, which I was not expecting, but it delivered 10 fold in what was already a great ride - However the upgrade is not for the 2005-2008 or at least no as of yet -
That may be the best suggestion yet. I have owned the car since 2006 and for all intensive purposes I love my car. The ride issue has been from the beginning. I do realize its a sports car and not a land yacht. But sometimes the ride on surfaces that are relatively smooth ride is OK but if there is paint on the road it can be felt.
To all:
I would like to thank all of you for your comments and input. I really do appreciate all the advice. I will take my car in and have it checked out by the dealer once again and see if they can help me out in any way. If they can't find anything wrong I will look for someone that with any luck can help.
I just bought a C6, after having a C3, C4, and C5 Z06 I feel the C6 drives great!! My 2012 only has 10k miles but I put new Michelin tires on this week due to the age of the original tires. The good ride got a ton better and less road noise with new tires; even though I did stay with run flats.