Should I only repair my blown overhead gasket on a 2002 Honda 900rr Fireblade?

Recently, I bought a 900rr from craiglist. I bought it knowing it had a blown overhead gasket (because the seller reached out to his mechanic last minute) and because of this new problem, I haggled down the price.
After buying the bike I took it to my mechanic for a full inspection on the engine just to be sure about the problem.
Later, the mechanic reveals a whopping 2500k service quote charge. 300 for the gasket system replacement (as I expected), 600 for a new radiator (coolant and water slightly mixed together) and they want to replace the engine.
Honestly, the engine runs great, I've gone 100 with the bike just to see how it fairs with the blown gasket and there's no compression loss.
My question is, I know a blown gasket can be caused by another problem. I don't want to get a new one only for it to be blown again.
Should I just get a new gasket system, or should I replace the radiator as well.
I'm no gearhead, but my thoughts are, if I fix the gasket, I can then just flush the radiator clean and put new antifreeze in it?
Should I just go ahead with the solo overhead gasket fix and not worry about the rest?

Added (1). Update: Forgot to mention the bike runs about anywhere from 200 to 280 degrees Fahrenheit after about 20 minutes of riding! So a blown head gasket seems very likely

There's something wrong with a mechanic that wants to charge you for head gasket work and also replace the engine, you think? You stated the radiator has coolant and water mix, that has to be a mistake because those two items always mix never separate. I'm guessing your saying oil and antifreeze mixed. That doesn't sound like a reason to replace the radiator to me. A flush would be in order. As for the head gasket, I'd question if the gasket is really bad or not, you said it runs good. But how hard would it be to remove the head and inspect it, the gasket is not that expensive and it would be a relief for you to know. If it is bad then you will need to check the head to be sure it is flat that is all that is needed.

Obviously you are no gearhead, there's a head-gasket but no overhead gasket and coolant and water is what is supposed to be in the cooling system. Your mechanic is trying to squeeze you.

Get a new mechanic, tell him you want the head-gasket replaced and than deal with it best you can.

Yes simple fix, head will have to be shaved to insure head is alright.

Your high operating temp in a short time indicates a bad water pump or a stuck closed thermostat. Either one will cause enough pressure to blow a gasket. I would look for both and repair whichever I found, then replace the blown gasket. A radiator flush is a given, replacement is not.

Get your bike out of that place As soon as possible.

>"After buying the bike I took it to my mechanic"

And that is the lesson you should take from this - change after for before. I would have walked away as soon as the owner made the admission over the gasket, at the very least you should have got some kind of estimate before buying.

Are you sure you have the requirements clear, it wasn't that the oil and coolant are slightly mixed (milky coffee coloured oil in sump) and that the engine would have to be removed from the frame to replace the head gasket? There could be a further cost if the hot engine has caused the head to warp - that involves machining off a slice of the head to get a true surface for the gasket to mate to - by which time the cost of a secondhand engine is often cheaper.

Someone is very confused… And it's not me.