I don't think a summer game will match the upticks of those November games in their second month. December is by far the strongest retail month, especially for Nintendo. Mario Kart 8 will probably fair better than Mario Kart Wii (which drop from the high 700s to low 300s even though it only had 5 days of sales in May), but I don't think that it will increase by 10-25%.
The issue with these predictions is that we're looking at an unprecedented situation for Mario Kart 8. The closest example we have to a few days of non-holiday sales is Mario Kart Wii, but even that isn't all that appropriate of an example because the Wii was a runaway hit with unique sales trends.
I believe that, in general, from looking at the USA sales history of Mario Kart and the strength of the IP, that 352K / 377K in two days represents a fraction of launch demand that we will see realised in the upcoming NPD month.
Applying an extremely loose extrapolation from conflating relative NPD sales to worldwide sales announcements:
"Mario Kart 8 has sold 1.2 million copies worldwide between May 30th - June 1st"
- Translates into 352K / 377K with NPD
(NPD's 377K represents approx. 31.4% of the stated worldwide number, but it's excluding June 1st)
"Mario Kart 8 has sold 1.2 million copies worldwide between May 30th - June 1st"
"Mario Kart 8 has sold 450,000 copies in the USA between May 30th - June 1st"
(NOA's internal figures represent approx. 37.5% of the stated worldwide number)
"Mario Kart 8 has sold 2 million copies worldwide between May 30th - June 27th"
NPD extrapolation:
(31.4% of 2 million copies is 628K)
(Or, an extrapolated 251K copies sold in 4-weeks in June, ~300K if extended to 5 weeks)
^ Lower than 377K May
NOA extrapolation:
(37.5% of 2 million copies is 750K)
(Or, an extrapolated 300K copies sold in 4-weeks in June, ~365K if extended to 5 weeks)
^ Lower than 450K May
I must stress that I was expecting bundle sales to be greater than last month. The possibility isn't all that great for June to surpass May...I'm just saying that it remains a possibility if the variables play heavily into Nintendo's favour because of the unique circumstances and the strength of the Mario Kart IP.