I just spent 4 hours messing with this myself and finally called HP and they hooked me up. I too have an 8600 and had the latest Full Service drivers, but could not get the scanner to work. I'm running Yosemite 10.10.1. The things the HP rep did aren't anywhere to be found. If anyone is having any more issues, try checking these things below.
First, I had just set up a new Airport Extreme (802.1AC) and I didn't notice that I was broadcasting ONLY on the 5GHz channel. Apparently the printer works on the 2.4GHz, so ensure that is enabled. Best thing to do is reset your network settings from the front of the printer once you make the change and re-setup your network wireless settings.
Start by (-) deleting your printer from the System Preferences/Printers & Scanners.
Install the latest Apple HP Drivers! This is nowhere to be found on the forums/internet. Here they are: HP Printer Drivers v3.0 for OS X
Without these drivers you will not see the 8600 with Bonjour Multifunction option (all I saw previously was simply Bonjour). It is important to see the Bonjour Multifunction or else you will not be the able to use all the features of the printer/scanner.
In your System Preferences under Printer & Scanners, (+) add your printer, let it run thru the setup/configuration. Do not choose AirPrint (instead choose the actual printer 8600).
Once setup and showing as a Printer, choose your printer and then Options and Supplies and choose Show Printer Webpage under the General tab. Once there, ensure two settings are changed (they are defaulted to the wrong settings during the install).
Go to the Network tab and under Advanced Settings on the left choose Bonjour and change Highest Priority Service from LPD to 9100 Printing (LPD is for Laser Printers). If you have a laser printer then leave this.
Next, under General choose Network Protocol and check Enable IPv4
only. IPv6 is generally for Commercial use. Apply changes and exit.
You may need to reboot your computer, but that should be everything...your printer should be working.
So frustrated to have gone thru this, but hopefully someone else can benefit.