I actually experienced this on my '12 MacBook air as well and it was driving me crazy so I think I've figured it out without having to buy any apps like smartsleep, etc.
So first off you need to look at how the Mac operates with its settings. The pmset command from Terminal shows and controls the settings. Don't change anything until you read the man page. Enter pmset -g in Terminal to see your current settings.
pmset -g | grep hibernate mode
hibernatemode 3
pmset -g | grep standby
standbydelay 4200
standby 1
Those are the defaults and you should read the full details on Apple's Man Page.
But basically what that means is after 4200s (70min) of regular sleep ("standby" on Windows), it goes into deep sleep ("hibernate" on Windows). From testing, wake from deep sleep takes about 3-4 seconds or up to 10 seconds depending on what you had open (all SSD times of course).
Now you can increase this time which means it remains in standby (aka memory is still powered). I have mine set to 42000s (700min) so that it covers most of my inactive scenarios (sleep, travel etc) and only hibernates on an errant weekend or two where I don't turn my computer on. Mac OS still creates the hibernate file anyways so you don't risk losing data. I have yet to test its affect on battery drain but maybe someone here can do that.
To set the standbydelay to 42000 seconds (11.66 hours), in your Terminal, type:
sudo pmset -a standbydelay 42000
and enter your password.
Now if you'd rather have it based on battery percentage there's a neat loophole. You see Power Nap basically also means that you have to keep standby active as obviously waking from Hibernate is inefficient. So when you check Power Nap on battery you are essentially keeping the computer on Standby until you hit 30% and then it will hibernate. This is because Apple set up Power Nap to do this so you can use this mechanism as well.
I've tried both and now my computer wakes quickly all the time.
If you've tried reinstalling and resetting PRAM / SMC etc and it's still occurring on a clean install then that rules out a software issue. If you've tried another ram stick that rules out faulty ram.
Sorry to tell you, but it sounds like a motherboard issue, which means $$$. That's the only other thing I realistically think could be causing the ram fault.
Best Answer
The greyed out (and blurred) background with the progress bar indicates that your computer hibernated (as opposed to suspended) - meaning it dumps the memory state to disk, and when resuming needs to restore that memory state from disk to memory.
To check which sleep mode your computer is using run the following from a terminal:
If it is 1, this would be the expected behavior. If it is 3, OS X is unable to resync the memory state from background tasks (such as time machine) and may fully restore the memory state from disk. If it is 0, the memory shouldn't have been dumped to disk during normal sleep which would indicate that it hibernated as a last resort before losing power.