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.
Best Answer
If you can get your MacBook back on make sure it's completely up to date, so that there are no more updates in Software Update.
Specifically make sure your Firmware is up to date, Software Update should catch this. If Software Update doesn't show a Firmware Update, then you can try downloading this Firmware Update directly from the Apple website: http://support.apple.com/kb/DL1098 If it's already installed or doesn't apply to your system it will tell you this and prevent you from installing it.
If that fails you can try reinstalling Lion. This is not as big of a job as it sounds. Turn off the Macbook and turn it back on, as it starts hold (before you get to the white screen) the alt key, and choose to boot into the Recovery Partition.
When you reinstall Lion it will download the latest copy of Lion (this can take a while depending on your Internet Connection*), and install it without deleting your files (the equivelant of Repairing Windows), though to be on the safest side you might want to backup at least your most important files, however I have reinstalled Lion in this way quite a few times without any loss of data. The actual instalation will take about 1/2 hour.
*If your connection is too slow, then go to an Apple shop, connect to their WiFi and do the reinstall there. They have local copies of the latest Lion OSX, so the download should be very fast.
Otherwise, the best thing you can do is to take it to an Apple shop, you can just go there with the MacBook and tell them and show them whats wrong (don't worry if it suddenly starts working as you walk in the shop, they will still believe you). They will do their best to help you.
You will receive the best service if you don't go in accusing them and hassling. Also try to avoid the busiest times of day if you can.
Even if you're out of warranty, they will help you, although you may have to pay for repairs if it's extensive and not a problem with the model, but sometimes you can get them to do it for free.