..... I don't even know where to begin.
Anything is possible if you throw enough time and money at it.
One man's 'minimal' is another's 'completely impossible'.... a lot of that has to do with time, money, space, and tools.
The cheapest way to put a running motor in that frame is to drop another like unit in there. If you want more power than a fresh motor would make, there are a number of modifications that can be made that will boost HP, but all of them will decrease the life of the motor.
Raising the compression, raising the redline, decreasing the restrictions in the air flow through the motor, valve work (port polish, degree the cams), cam work (racing cams), turbo charging, nitrous.... the list is long, of what CAN be done. Almost all of the mods will be more expensive than the bike is worth.
The reason it's so tough to drop in another bigger displacement motor into the 600 frame is due to the desire to make it as light as possible. The frame is no bigger than it needs to be. The motor is already at or nearly at the maximum bore and stroke it can be. You need a physically bigger block to increase the size of the pistons used. The 09-13 motor, and the 13-present are the same outside dimensions. It's the same motor; the 13+ version has had a stroker crank fitted from the factory. That much work, and it only grew by 36 cc.
They did a bunch of stuff to simplify the design as well... there are only one set of injectors now, compared to the two sets on the 09-12. Very nearly the same motor. Just a bit more power, and a slightly lower redline. More midrange.
If you want to have a more powerful bike, the most sure way to do that is buy one that already makes the power you want. Let the engineering staff at the mfg do the heavy lifting.
The second most sure way, is to build a motor before you drop it into your frame. Have someone like RiversZZR go through it top to bottom and make sure it's right. Someone with a racing/performance background is going to be able to eke out more power than the factory was allowed to, due to the EPA. The more money you spend, the more power you will get. A lot of it's in the details.
If you grab a used motor with an unknown background, and don't even know if it will fit in your frame...... you are going to throw a lot of money at a situation that will end up taking a lot more time and money to make right.
If you DO manage to stuff a motor that weighs quite a bit more in there, how will that affect the suspension? How will the additional power (and weight) affect how much the frame and swing arm flex?
Once you do get it in motion, and get it going too fast, how good are your brakes at dealing with the additional weight and speed?