If you don't want to get the lime, that amount of baking soda is fine (i've used comparable amounts and it's come out very well on the other side).
In general your water profile is good. I would personally lower the bicarbonate. I typically target a profile in this range (bicarbonate as high as you have gives a weird minerally mouth feel I find):
125 Ca
5 Mg
50 Na
100 SO4
150 Cl
250 Bicarbonate
As far as the recipe, like others, I would recommend simplifying it. You by no means have to, i'm sure this will turn out a nice recipe, but 1 crystal malt is fine (probably the 80, I personally love 120), one of either munich or vienna, no need for unmalted barley. You can probably get it down to 6 malts without much effort.
Best of luck!