If your frame is still JIS, H/T ID just under 30.0mm, you have two choices for a proper job.

get a true JIS headset that will work, and I can help you there, as I have some nice Low stack JIS (27/30mm) SunTour Superbe Pro track headsets (very old stock), which should meet your needs.

Or have the head tube properly reamed to ISO 30.2mm (+0.0 -0.05), by a decent shop. This shouldn't be expensive and will give you access to a wider selection of headsets going forward. While you're at it, also have the fork crown hollow milled to 26.4, so you don't have to hybridize headsets.

As to whether a 30.2 cup can be pressed into a 30.0 frame, the answer is maybe. Steel is very ductile, and if the frame is a typical welded frame with a thin headtube and no ring at the bottom, it'll probably be OK. But on a lugged frame the added wall thickness will make the frame too stiff and the pressing load excessive, possibly cracking he headset cup (especially if it's aluminum). For carbon frames it's definitely impossible and will crack the frame, and aluminum and Ti are in between and will either crack or give depending on the temper (something you're not equiped to measure).

With respect to Park and anyone saying flat out that it's OK to press a .2mm oversize cup into a frame, they're just plain wrong. The correct level of interference is .05mm, based on a steel lugged frame with a wall thickness of 2-3mm. For steel without the band, or aluminum up to about 3mm, Ti up to 2mm you would want more interference to compensate for the weaker (stretchier) tube, so maybe up to .1mm, but .2mm well above standard specs.