First, you are doing a partial boil and then topping off with almost half of your batch size. Hop Alpha acid isomerization is dependent upon the gravity of the wort, with the higher gravity impeding the isomerization of the hop acids. Since you are limited in your kettle size, then I would recommend adding half of your extract up front and then adding the remainder with 5 or 10 minutes left in the boil. This will help with utilization of the early bittering hops and should be reflected in the IBU number
Next, I didn't spend much time on the Briess site looking up the way they calculate the IBU numbers but they may be using a different IBU model than you are using. If you are in default BeerSmith settings, it is set to use the Tinseth model. You can change this through your 'options' settings from Tinseth to either Rager or Garetz, but without knowing which model the recipe follows, this would be just cherry picking to get the numbers to match. IMHO, you are better off just sticking with the Tinseth model as I have found it to be more responsive than the other models and better matches the apparent bitterness in my brewing process.
Lastly, I never sweat the IBU numbers from recipe to my system. Too many people don't specify the model they use nor do they specify the volumes through their system to allow me to make adjustments. So, I match each addition for AA units (amount of hops times %AA of the hops) and brew on. Once I have brewed a recipe with my system, I can adjust the bitterness up or down the next time I brew it depending upon how I want the bitterness to come out in the finished product.