I've not tried this personally in this exact situation, but you should theoretically at least be able to add a new point at the correct location (leaving the attributes blank). Then go to the attribute table and select both rows (the newly created point without attributes and the corresponding attribute record without a point). Then go to the Editor toolbar and click the Editor drop-down menu and select the Merge... tool (this is NOT the same as the Merge Geoprocessing tool). On the resulting merge tool box you should select the record of the row with all the attribute data (they should theoretically be listed in order of their OID/FID field).

Ideally that should basically just append the geometry of the new point to the existing attribute record. Hope it helps.

I've not tried this personally in this exact situation, but you should theoretically at least be able to add a new point at the correct location (leaving the attributes blank). Then go to the attribute table and select both rows (the newly created point without attributes and the corresponding attribute record without a point). Then go to the Editor toolbar and click the Editor drop-down menu and select the Merge... tool (this is NOT the same as the Merge Geoprocessing tool). On the resulting merge tool box you should select the record of the row with all the attribute data (they should theoretically be listed in order of their OID/FID field).

Ideally that should basically just append the geometry of the new point to the existing attribute record.