It may not be the same thing as you are experiencing but I have noticed a lot more sticking tasks since I changed from 3 to 2 GPU cores. A lot of the tasks now have 13 packets instead of the standard 12. With two cores and an uneven number of packets, one core is idle and goes to sleep while the other core finishes the final packet. Trouble is the idle core often doesn't wake up when the task is finished and so the next task is done on only one GPU core. So instead of taking 8 minutes it takes up to 20+ minutes and sometimes doesn't even complete the full number of packets but just sits there frozen until the watchdog timer ends it after 20 minutes or so. I suppose a similar thing would happen with the smaller tasks sent to 4770s, compared to the ATI_5K tasks sent to HD 5xxx cards, the number of packets is the same just half sized packets.
It can slow your CPU projects too because after a task is frozen an extra phantom dnetc_1.31 windows_intel86_ati13exe*32 process may remain running which consumes a full core of CPU processing. If you notice a sticker you need to end this process if present (the one using a full core not the normal one using 0-1% CPU) in Task Manager and then suspend and resume DNETC in BOINC Manager. Sometimes have to do it twice before you see the second GPU core start up in Afterburner. This is for one stuck using only one GPU core near the start, if at the end of a task then only one packet may remain to be processed, so in that case only one GPU core would start or for "end frozen" tasks they may unfreeze and complete almost immediately. GPU temps will show if only one GPU core is being used by DNETC.
If you are doing something else or asleep just have to cop it sweet, DNETC has always been a bastard on multiple GPUs and they aren't going to fix it. Some have found different Catalyst driver versions to be better than others for stickers. Generally speaking it seems more likely to happen when the screen is turned off even with a dummy plug fitted. Without a dummy plug there is a much higher chance of trouble when the the screen is switched off in my experience. When I was running 3 GPU cores the watchdog timer kicked in after 10 minutes but now with 2 cores it takes just over 20 minutes. Looks like the watchdog timer kicks in around 2450 seconds on your pair of 4770s.
I'd prefer to do MilkyWay even though the credit is less. It's just that I am currently fed up with the way they feed their server. They load it up with N-Body tasks and then go home and it backs up and malfunctions just about every day. I'll probably go back to it in a while when I can once again cop their slackness. ;D