To find what you want faster, you have to broaden your search criteria.

Either increase the distance you are willing to travel or the time you are willing to wait. Choose one.

I sold an 01 Z mid July and bought an 04 Z mid August.
I was casually looking for an 04Z for about 4 months, saw some great deals that I had to pass on (because I hadn't sold the 01Z). Once I sold the 01Z seemed like all good local deals dried up.

I looked on Craigslist, Corvetteforum, Autotrader, and Cars.com. Daily. Sometimes hourly.

I had to have an 04Z, color optional, under $23.5k.
The exact car I wanted (04Z Z16 24h LeMans edition) was listed for $23.5k with 55k miles and sold before I sold my 01Z. That hurt.
Another 04Z16 came up for sale for $22.5k with 42k miles, but 900 miles away, so I ignored it. Would have been a great deal if I would have driven that far. All other Z16s were $26k and up.
A red 04Z came up for sale at a dealership for $26k, but was dropped to $23.3k over the course of a month. But the carfax said 6 owners, and OK most of them were dealers, but this was too far removed from an owner with any knowledge and history of the car.

So finally I found a silver 04Z 350 miles away listed here on CF. Asking $23.9k, 47k miles, and 1 year left on GMPP warranty. We both agreed on a deal and I took the train up and drove it home.

Another thing to remember, anybody listing their Z06 for anything near KBB is dreaming. NADA values are more realistic. Edmunds is too low I'm afraid. But again, market value is by definition what one person is willing to pay and a price the seller is willing to let their car go. When it comes to the Z06 market these days, many sellers are having to wait months, and likely bring their prices down to get near market price.

But don't compromise on the car you want.

 

I just picked up my 17.5k-mile 03 Z06 with MS3 cam, PRC Stage 2.5 5.3 heads, RHS/LSXR 102 intake manifold, Halltech air intake, Kooks longtubes and ORX, SLP Loudmouth axleback, and black C6Z replica wheels wrapped in new KDWs for $25,750 (NADA dealer retail stone stock is $25,700, so I got all the mods I would've done anyway for $50) at a dealer and feel like I bought the car for its value. Swapped the straight pipes for factory titanium mufflers and looking to get it tuned and she's good to go by the way, the car was nearly 1000 miles away, I just incorporated the test drive and pickup into a road trip vacation for me and the wife.

 

Definitely expand search...it's harder to inspect, but if you find a good owner, you'll get lots of detailed pics and records before you even have to take a trip out there. I used autotrader and craigslist. Autotrader was a joke...everyone was holding out for 24-28k for 02-04z's, so I started looking in surrounding areas craigslist. I found a bunch cheaper, but most were bling-bling rimmed up with all sorts of mods and stereos. I was just looking for a good unmolested car. I sent one guy an email about his 02 EB Z06 and he replied a few days later stating someone was going to purchase in the next week. SO, I was deflated and moved on to the next one. Well, the next one never came and i couldn't get what I wanted for less than 25k. So after browsing autotrader for the 100,000th time, i got an email from the guy in NC who said it was sold...he said the old buyer backed out...you want it? He was getting divorced and had to get rid of assets...lucky me! I carfaxed, got pictures and records...talked to him for about 2 days...bought a plane ticket and flew up the next day...drove home 500miles the next day a very happy man!

Everyone that says be patient, is right! I eventually got what I wanted and for $22k, he was asking $25k orig. Super nice guy...felt terrible for him going through the divorce. It isn't a showroom car now though!

Good luck and hang in there!