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Have you done extensive international travelling before? Going to Japan from the DR is not a typical first trip and I would raise huge red flags. Not only is it an expensive country to visit it is on the other side of the world. If you haven’t had significant travel history it will be assumed that you are trying to get into Canada via the transit visa. It is also very unlikely that it is cheaper to fly through Canada. Flying through the US is likely less expensive.

This . I did a random price check . Flights originating from the USA to head to Japan are typically priced cheaper thru Canada since Air Canada wants to funnel passengers from that huge market thru Canada . The American market is massive , compared to Canada . DR traffic would be not cheaper , nor faster .It would be such a SMALL point to point traffic , it would be more expensive . No deals in other words .
Volume makes tickets cheaper . Traffic exiting North America from the eastern part all go up and over Canada , Alaska then down .
And the USA no longer has transit visas aka TWOV. They were abolished after 9/11 due to security concerns and rampant abuse by travellers disappearing in transit.
Getting a visa appointment for the United States is an EXTREMELY long wait . The gf might have to meet you in either DR or a third country where you don’t require a visa