I really do not like taking the papers out when paper piecing. I love the method for some blocks. But for a log cabin where there are no "points" ... I would starch my fabric prior to cutting ( I use a pretty heavy starch). Then cut my strips. I make log cabins with strips as narrow a 1 1/4 inch . For me it goes much faster than P/P and I can get very accurate using starch( be very generous) and my 1/4 inch foot.
Starch tip- use the Stay - flo concentrate in the blue bottle ( I find it at Walmart in the laundry section) dilute it about 2 parts water to 1 part starch. I dip the fabrics in... let it saturate , use a drying rack for drying. then iron. You will be pleasently surprised at the difference it makes in the final results. This part takes a bit of time ... but soo worth it. Once I have it starched , ironed and cut ... I am off to the races so to speak... It goes so fast then.
I find the accuarcy is so good I have not had to square up till the end and then it was so minimal it was non -existant.