The ISO crown race inner diameter (26.4mm) is smaller than the JIS (27.0mm) crown race inner diameter. You will have a hard time cramming it on the original fork.
As temporary measure, until you get the new fork, you should be able to keep using the original fork with the original JIS crown race in the new ISO headset without too much trouble. Although this could depend on the headset models and dust seals might not fit right.
Alternatively, why ream the frame at all? Just use an ISO crown race on the new fork. Leave the rest of the JIS headset in place...