On July 30th, Nintendo is scheduled to give their Three Months Earnings Release for the 2019 Fiscal Year.
https://www.nintendo.co.jp/ir/en/schedule/index.html

And obviously, the fun with that is they will be giving updates for all of their hardware and software sales, particularly the Nintendo Switch. In 17 days, that list is going to be altered and edited to reflect Nintendo's latest figures as of June 30th. So with that, it's PREDICTION TIME!

These are Nintendo's Switch hardware and software figures as they stand as of March 31st. (In parentheses and bolded will by my prediction for the updated figures as of June 30th) 

Nintendo Switch: 34.74 million units of hardware (37.20 million); 187.52 million units of software. (220.50 million)

Top 10 Best Selling Titles:

Mario Kart 8 Deluxe - 16.69 million (17.8-18.1 million)

Super Mario Odyssey - 14.44 million (14.9-15.2 million)

Super Smash Bros. Ultimate - 13.81 million (15.3-15.6 million)

The Legend of Zelda: Breath of the Wild - 12.77 million (13.4-13.7 million)

Pokemon Let's Go Pikachu/Eevee - 10.63 million (11-11.3 million)

Splatoon 2 - 8.70 million (9-9.2 million)

Super Mario Party - 6.40 million (7-7.3 million)

New Super Mario Bros. U Deluxe - 3.31 million (4.3-4.7 million)

1-2-Switch - 2.97 million (3.1-3.3 million)

Mario Tennis Aces - 2.64 million (2.7-2.8 million)

I think you're overestimating the Switch a bit here. While the sales are up compared to last year in the same period, it's not by that much. Also you're expecting very much out of the game sales, but close to 2M during April-June seems way too high for me.

That said, here's my prediction:

Nintendo Switch: 34.74 million units of hardware (37.90 million); 187.52 million units of software. (216 million)

Top 10 Best Selling Titles:

Mario Kart 8 Deluxe - 16.69 million (17.4-17.8 million)

Super Mario Odyssey - 14.44 million (14.7-15.2 million)

Super Smash Bros. Ultimate - 13.81 million (14.6-15.2 million)

The Legend of Zelda: Breath of the Wild - 12.77 million (13.0-13.4 million)

Pokemon Let's Go Pikachu/Eevee - 10.63 million (11-11.4 million)

Splatoon 2 - 8.70 million (8.9-9.3 million)

Super Mario Party - 6.40 million (6.6-7.1 million)

New Super Mario Bros. U Deluxe - 3.31 million (4.1-4.8 million)

1-2-Switch - 2.97 million (3.1-3.3 million)

Mario Tennis Aces - 2.64 million (2.7-2.8 million)

Bonus: Super Mario Maker 2: 2.8M, kicking MTA out of the Top 10

2,9 millions shipped (2,612 estimated sold by VGC + 0.3 M restock)

I wonder how you can estimate that much from 2,612, knowing that they would rather dry a bit the stock of the current model to anticipate with the coming Lite model.

I'm expecting a number for Yoshi and Mario Maker to add them to the Wikipedia count list of top sellers, and I wouldn't be entirely surprised if I saw something about Mortal Kombat's sales after it topped a month for Switch. But that's about it on my end.

My prediction chart:

Mario Kart 8 Deluxe - 16.69 million -> 18.1 million

Super Mario Odyssey - 14.44 million -> 15.2 million

Super Smash Bros. Ultimate - 13.81 million -> 15.3 million

The Legend of Zelda: Breath of the Wild - 12.77 million -> 13.6 million

Pokemon Let's Go Pikachu/Eevee - 10.63 million -> 11.2 million

Splatoon 2 - 8.70 million -> 9 million

Super Mario Party - 6.40 million -> 7.1 million

New Super Mario Bros. U Deluxe - 3.31 million -> 4.2 million

1-2-Switch - 2.97 million -> 3.1 million

Mario Tennis Aces - 2.64 million -> 2.74 million

Super Mario Maker 2 - 3.5 million

Switch Hardware - 34.74 million -  (+2.9 m) 37.64 million

Mario Kart 8 Deluxe - 16.69 million - (+1.6 m) 18.29 million

Super Mario Odyssey - 14.44 million - (+0.6 m) 15.04 million

Super Smash Bros. Ultimate - 13.81 million  - (+1.5 m) 15.31 million

The Legend of Zelda: Breath of the Wild - 12.77 million - (+0.8 m) 13.57 million

Pokemon Let's Go Pikachu/Eevee - 10.63 million - (+0.5 m) 11.13 million

Splatoon 2 - 8.70 million - (+0.3 m) 9 million

Super Mario Party - 6.40 million - (+0.7 m) 7.1 million

New Super Mario Bros. U Deluxe - 3.31 million - (+0.7 m) 4.01 million

1-2-Switch - 2.97 million - (+0.1 m) 3.07 million

Super Mario Maker 2 - 2.8 million

Mario Tennis Aces gets bumped off the top 10 best-sellers. I expect we'll get an update for Yoshi's Crafted World - (+0.4 m), 1.5 million.

Rebumping with the updated figures due in 5 days.
Taking a second glance, I think I overshot my original predictions, so I moved my hardware prediction down to 37.20 million. I also adjusted my predictions for Mario Kart 8 Deluxe, Super Mario Odyssey, and Breath of the Wild slightly down.