We have one set of stairs in the house we're remodeling that run completely between two walls...no balusters at all.. At first I wanted to make them wood treads with painted risers but was getting quotes of $1500 or more (15 steps)...and we have an old dog that follows me everywhere and she'd slip on wood steps so I'd probably carpet a runner anyway...so I'm going back to recarpeting them...the previous owner had berber carpet but the stairs are completely boxed. There is no overhang at all from the tread to the riser...a carpet man told me to adhere a 2x2 at the edge of each box...then carpet over it...I like that idea but will that work? I could wood glue/screw them in tight and securely but would the 2x2 need to be bull nosed for the carpet to wrap around right? Is leaving a squared edge sufficient? Would the type of carpet I use make a difference? I just want one that won't show wear as much as others...was thinking of a tight commercial grade (hotel type carpet) but then thought a plush might make it look more bullnosed if I don't router the edges?

Please share any tips!

Tara