Yes, a 275/60/15 will fit the rear. The rim backspace will determine where the tire sits in relation to the frame on the inside & the wheel arch on the outside. You already have the rims so that's already been decided. Spacers are not recommended for changing backspace because they move the load outward on the studs, although there's always plenty for sale on eBay & people using them I guess too.
I'm guessing your white wall tires are a 70 profile? Go to the website for your white walls & find out the o.d. of the front tires, then go back to the MT webpage I pointed you to in your other thread & find the front tire that best matches the o.d. of your current tire. And that will be about as big as you'll get because in your pic the front tire gets quite close to the fender on turn in.