The HTSUS permits only two special program indicators to make a NAFTA claim: MX and CA. To make a legally valid preference criterion E claim at the time of entry, you have to use one or the other. But in the example of the Japanese computer, the CO must be accurate and valid. The CO, therefore, should probably correctly state the fact the origin is JP because the NAFTA marking rules don't result in a NAFTA country being the country of origin.
Certain automatic data processing goods and their parts, specified in Annex 308.1, that do not originate in the territory are considered originating upon importation into the territory of a NAFTA country from the territory of another NAFTA country when the most-favored-nation tariff rate of the good conforms to the rate established in Annex 308.1 and is common to all NAFTA countries.
An alternative approach that avoids this problem, but has cash-flow implications, is to avoid making the claim at the time of entry. Instead, make a post-entry claim for a refund. That way, you don't have to assert a NAFTA country as the origin in the SPI column (although it can be argued that the SPI is not an origin claim but only a duty preference).