All electronic signalling switches have signal bounce, it's a law of physics. The solution to signal bounce has to happen at the engineering design level, in the design of the switch, and the programing of the keyboard controller, and the design and construction of the PCB. Every person who designs a keyboard knows (or should know) about signal bounce. Since you have thoroughly cleaned your keyboard, you have eliminated dirt and hair as a factor (and proven that it is not user error). So the problem is most likely a manufacturing defect in the PCB or the controller. If the switches are authentic Cherry switches, they are probably not the problem (it is highly unlikely that 4 or 5 Cherry switches have all gone bad at the same time). However, in China there are counterfeit Cherry switches, so who knows what you actually got. But basically I think you got a bad keyboard that does not eliminate signal bounce due to a defect in the PCB or the controller.
The answer is to get a different keyboard.
I think you might want to get a more reputable keyboard that has a decent warranty like a Leopold or a Filco.
For $99, you cannot go wrong with this Leo with MX reds:
http://elitekeyboards.com/products.php?sub=leopold,tenkeyless&pid=fc200rrab. I have this Leo FC200R, and it's really great. You can save $20 by buying a cheaper keyboard, but you have already seen what can happen with that option.
A better choice is to go with a capacitive switch like the Topre, which is a completely different (and IMHO a superior) engineering solution to signal bounce. However, it will cost you three times as much. However, if you like MX reds, then you will absolutely LOVE a variable weighted silent Topre RealForce, like this one:
http://elitekeyboards.com/products.php?sub=topre_keyboards,rftenkeyless&pid=rf_se070s. Only problem is that it will cost you $265. However, you are getting one of the best keyboards in the world, with a great warranty.
If you want 60% form factor, and want to spend $260, then go with the HHKB Pro 2:
http://elitekeyboards.com/products.php?sub=pfu_keyboards,hhkbpro2&pid=pdkb400w. Either keyboard is great.
Now, I know you said you want to spend around $80, so why am I telling you to spend three times that amount? Because I have learned over time that spending the money up front will actually save you money and frustration over the long term. Just get the best in the beginning, and you will save a lot of money you would have otherwise spent climbing the learning curve. Profit from my experience, please.