Not only are good runners expensive, I think you would have a real problem with tripping on the stairs. I have had 2 wool runners installed in 2 houses and both times the installers said that you have to be careful with the thickness of the rug pad underneath because even a fraction of an inch can throw a person off balance (we are so accustomed to a particular stair height). Just a thought...

Just to be sure of what you want - Your stairs are carpeted now, and you want more carpet to put over them? That could be a hazard for someone not used to walking on them, with the increased thickness.They would have to be attached with carpet tacks just like the ones you have now. You can rent a rug cleaner or have someone come to your house to clean rugs, which may be less expensive and will be safer than a heavy runner on top of existing carpet on stairs.

If you paid for a 'retread' then you might only get new wood on the treads. If you paid for the spindles to be removed, the Red Oak removed and replaced with matching white oak, then you have a right to be upset. It all depends on the contract. Stairs are tricky. They are expensive, they are tiring, they are tricky and then are (once again) expensive. **If your original talk (ie. contract) spoke about staining, the GC (not a wood professional by any stretch of the imagination) would assume the two woods could be matched once stain went down (very common to work this way). If you then changed your mind and went with a natural finish, the Red Oak stringers became a liability that never were properly addressed after that (ie. paid for removal). Did your GC use a finishing Carpenter? If s/he did not, the GC was saving money. What used to be on the stair treads? Do you have photos of before (old coverings) and after (new wood with finish)?

You don't need to remove the quarter round if you do a water fall installation that just folds down over the the nosing and then is attached at the back corner of the riser and tread. If you are talking about where the staircase transitions from an open riser and railing to where it is a closed riser and a wall, I would Not step the width in. I think the uniform appearance of the runner from the front is more important than exposure of the tread being equal on treads that vary in width. In my area custom binding that much carpet into individual stair treads would be expensive. My bound rugs, one of which has a shape other than rectangular, the binding was charged by the linear inch.