An engine swap is very easy on these bikes; biggest problem will be getting old exhaust manifold nuts off the studs without snapping them.
This will not matter if you are swapping engines.
I was going to mention the replacement engine warranty period but considered you had enough to digest in the reply.
Do not even consider heavy parts from USA; the carriage and also import tax from non E.U countries will be crippling.
A motor for $1600 dollars is very expensive; a complete bike in UK would be $830 ish (see link)
http://www.ebay.co.uk/itm/Yamaha-fzr-600-/141239131448?
This has not sold for the past 3 weeks.( come over for a weeks holiday and ride it home )
You do not need tremendous mechanical skills to swap out a motor; far less than repairing the existing.
You will need access to sockets and wrenches though.
The motor can be supported on wooden blocks and if the rear engine mount bolt is then fitted, it just pivots up into place.
Take lots of pics when you strip down the bike for reference .
I thoroughly recommend the Clymer Fzr 600 manual;
http://www.ebay.co.uk/itm/Yamaha-FZR600 ... 2336d16dc4
Avoid the Haynes; it tries to cover too many models with not enough specifics. (useless for beginners)
I would not recommend using any other carbs but 3He originals.
The fueling on these bikes is very precise.(not like swapping a Webber for some old car carb)
Don't get mixed up with Yamaha 600cc bikes;
The Fzr 600 3HE ;the Fzr 600 4JH Foxeye called the YZF 600 in USA and the "true" YZF 600 (R6) are completely different bikes,
Example of price for 3HE motors in Europe;
http://www.microsofttranslator.com/BV.a ... 51b7d23429
http://www.ebay.co.uk/itm/YAMAHA-FZR600 ... 3cdf1db0f7
You say you know what is wrong with you engine !
But do you ?
If it is using that much oil; it may need pistons and a rebore = not financially viable.
It may just need valve stem oilseals but it will cost a head gasket (£35) just to look.
Can you get a compression test done on it ?; if the readings are low/vastly different between cylinders then forget it.
Sent from my keyboard using the English language not some teen text shite from a fooking phone.