cheeeeee
Yes, the Steinway sound absolutely has a lot to do with the design, not just the hammers.
How a specific Steinway sounds with the soft pedal engaged has many effecting factors not limited to the type of hammers and voicing. There is also the adjustment of the pedal mechanism so that just two strings are struck in the trichords when the pedal is fully engaged. This really changes the sound character (the felt is less compacted there than in what are usually the beginning of grooves in the normal position), as well as making it considerably softer. So, in a way, when you play with the soft pedal fully engaged on a piano adjusted properly, you are playing on felt very similar to the way it was when first voiced.
Regarding getting a different piano and putting Abel hammers or something similar, may I suggest you have a look at Kawai vs Yamaha? If you Google Daniel Grimwood, he is an English concert pianist who recently has been using his own piano (a Kawai) in concerts. To my ears, it has a very nice sound indeed. I think it is a 208cm or something similar to a "B" in size.