Between the BLR and the Model 7, I'd take the Rem. model 7. But, like Portage, the stock doesn't fit me too well either. It's a good rifle, but just not for me. Check one out, and see how it fits/feels to you.
Other alternatives might be the Ruger Ultra-Light, which also has a 20" barrel, and is available in 308Win.
Also, take a look at the Winchester Featherweight with the walnut stock and stainless barrel/action. Available in 308Win. with 22" barrel (can always find a 'smith to cut the barrel back a couple inches and recrown, for maybe $40+/-).