Your trip the Genius bar was too focused in my opinion. I suggest you make another appointment and lay out your case above, but this time, don't mention the memory tests, but that the problems showed up when you upgraded the RAM. Refer them to your old case number (tack this visit on as a follow-up).
Tell the Genius on hand that the problems still exist and that they need to do further testing. As it stands, your Mac is unusable. Additionally, tell them to make note that you have tried a fresh re-installation and it did nothing to help (don't mention that things ran fine for a day or too, stick to the current state of the system), which will rule out any software problems.
Ask them on what they suggest and follow it (no matter how annoying it may be). If it doesn't fix it, call them and do another follow-up. If they tested the RAM and it passes, then it might be the logicboard.
In any case, do not visit them with "the solution." Let them find it through there own testing. Clearly, the logs containing kernel panics and all the problems you list will support your case. Moreover, their internal testing tools are much more sophisticated than what you'll scrounge up on the net through 3rd party apps (they actually have in-house diagnostic utilities for these occasions).
I would highly recommend that you stop spending your time diagnosing the problem and let them do it for you. That's what they're there for.
If after everything is said and done, and they still can't pinpoint a problem, you will likely walk away with a new Mac. Just focus on the problems you are suffering from and leave the diagnostics to the Geniuses and technicians.
You may want to downgrade back to the 4 GB for now. And it's of note that replacing the RAM and the hard drive yourself do not void your warranty for that particular Mac model.
PS: You don't specify if you took your notebook to an Apple Store and spoke with a Genius or some Apple authorized repair centre. I would strongly encourage you to deal with Apple directly. They'll not only treat you better, but likely solve the problem with less headache. My advice is tailored to them; you are totally on your own should you choose a 3rd party repair shop. To galvanize the need to deal with Apple, let me put forth the following. I had a friend who purchased a Mac mini. There were strange problems during boot up where it would occasionally load the keyboard set-up assistant. The machine was also sluggish and exhibited other unusual anomalies in its day to day. We took it into an Apple Store and the Genius tried to reproduce the errors. He couldn't. He also expressly stated that minis never required repair or servicing. But with all that, he elected to replace the entire unit and gave my friend a new mini. Took it back to his place and it hummed, no more issues. I doubt he would have received the same treatment from a computer store authorized to service Macs. Deal with Apple direct; I cannot stress that enough.
My mid 2010 15 inch Mac Book Pro is in for a logic board replacement right now for what looks like the same issue. At least the first line of the log you posted is identical to the ones I was having. Apparently a run of nVidia graphics chips used in that vintage of 15 inch MBPs had a "latent defect". The bug can be tickled or not depending on the applications you are running and also the OS revision -- different releases of OS/X use the graphics hardware in different ways. My panics really got bad after upgrading to Mavericks, like yours -- though I had a few, very few and far between (<< 10 in all) before the upgrade.
When you take it in to Apple, be sure that they run what is called the VST test. The Apple stores do NOT run this test routinely even though it only takes a few minutes. Even after telling the Genius who took my machine in that I wanted this test run, and even after the test appearing on the work order, they did not run it until I insisted over the phone (their recommendation was to wipe the disk clean and do a fresh OS install). This was after they had run every other diagnostic on it for two days and pronounced the panics software related. Of course, it failed the VST test, and as I said, is now having the logic board replaced.
BTW this is the TS4088 issue, and although you should be within the 3-year window or just barely out of it, many Apple stores will still pick up the tab for this since it is a known problem.
Good luck.
Best Answer
Suggested problem tracing /and repair) steps (after each test the performances).
Some applications will force use the Nvidia card (without automatic switching).
Yes the ZOOM feature adds stress to the GPU.
Vacuum clean the inside of your Mac to improve cooling.
Google and Install gfxCardStatus, Leave on Dynamic Switching. From there it will Monitor and Alert you to what apps switch you to the Nvidia Graphic Card.
Also open the Activity monitor - Energy tab, where you can see when the Nvida card kicks in, and does it switch on/off irregularly.
Monitor your Console log for irregular (fast)GPU switching.
Do some hardware testing: