Multiple entries in Japan question

Hi all, I'm planning a two-part trip to Japan soon and have been worrying about whether the schedule might raise suspicion from immigration or not.

For context, I'm a EU citizen. I'm going to Japan in May for about 7 days to look for accommodation for the summer and spend some vacation there. Then I'm going back home for about 3 weeks before travelling again to Japan in June this time for a 3-month summer internship, unpaid and falling under the 90-day temporary visitor time span. However I accidentally booked my flight to a slightly too early departure date and considering the 90-day count starts on the next full day after arrival, I'm about 2 days short to cover the full internship duration.

I was thinking about attempting a "visa-reset" workaround by taking a weekend trip to Korea and going back to Japan either early into the summer trip, or after a month or so, or slightly before the 90 days permit expires. But as this typically looks like a visa run scenario especially with the latter, I was wondering what were the odds that I might get flagged by immigration and be denied re-entry ? Are there significant risks even if I'm able to prove I have a return flight back home ?