Different studless winter tyres per axle

I'm in Japan, and approaching winter means one has to get winter tyres (will get in to trouble with Police and insurance company)

My car (BMW 5 series X drive) has 245/40r19 on front and 275/35/r19 on rear.

I can't find a manufacturer that sells winter tyres (specifically 'studless' as I'll be taking into snow resorts) in both these sizes. So someone who sells 245/40 doesn't do 275/35 and someone who does 275/35 doesn't do 245/40.. (or rather my googling hasn't found one)

I figure my options are :

a) buy some for the front with some and for the back and not be concerned about the mix

b) buy new 19" 'winter' wheels with tyres that are the same. However my issue with this option is I'll only be staying for about 12 months before taking the car back to Australia with me.. that doesn't have a too much need for winter wheels and tyres.

Any tips / thoughts / advice on going with option a of two manufacturers?

Thanks

Yep. It's what's on there at the moment, and having a quick look, the sales brochure says

1UX
M Light Alloy Wheel Y Spoke Styling 845M Bicolor (Jet Black)
(Front) 8J x 19 wheels + 245/40R19 tires 
(Rear) 9J x 19 wheels + 275/35R19 tires

Not an SUV or off road vehicle, is a 5 series