Gear won’t fit back on shaft

If you happen to have an induction cooktop those work great for this!

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For that diameter, you should be able to get .0015". For insurance, I would throw in the dry ice if I could easily get it.
 
I have my lathe spindle removed and need to reassemble it. The problem is that the gear which is keyed, is a press fit not a slip fit and it is impossible to perfectly align the keyway. You can see in the photo where the gear was damaged by forcing it over the key. I see two options, I can either heat the gear to expand it and hope I can reassemble the spindle before it shrinks or I can cobble together an ID grinder using the mill and rotary table. The shaft is 1.9695 and the gear is 1.9680 Obviously, heating the gear is easy and low risk other than burning my fingers but I am uncertain if it will expand enough. The gear seems to be hardened and the ID may have been ground, it has a very nice finish. Any ideas or advice?
If you can find someone with a tank of liquid nitrogen and warm the gear to 250-300 you can put it on and line it up before the temps equalize enough to lock it down.
 
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