I am really new at this long range stuff too, but to me, high bc bullets moving fast is how to get it done. I couldn't find any info on the 7-300WM, nor does the Hodgdon online data site list the 7mm 195gr SMK. However the 180 7mm in the 28 Nosler leaves the barrel at (max listing) 3050fps. Just at a guess, the 7-300 might do better.
Roy was not happy with the 340, from what I have read. He only bested the 338WM by a small margin. The company later necked the 378 down to 338cal, and it Smoked the 340. Hodgdon does not show a listing for the 300gr 338 SMK in a 340, and what I saw was really slow, even max listing. I would go for it. Just saying.
Gregg