Hello and welcome to the forum! \\
Very nice scenario you've presented above.
For my part, in the given conditions (18000y battle with no previous hit on either ship) the Tirpitz would have the advantage, as hes rate of fire was better, danger space was better and salvo gropuing was better. Practicaly all the sections of Iowa wold be directly vulnerable to 38cm shells, with the only exceptions of the main magazines (well below the waterline and very well protected) and main turrets. The other essential compartments - ploting rooms, con tower, secondary magazines
, and their redundancies would be easily destroyable by the German guns. I see Tirpitz vulnerable from the panzer-deck upwards. No section above the panzer deck can withstand 1,22 ton L50 shell hits (with the posible exception of the main communications tower). However, the ploting rooms and communication tubes would be difficult to take out by Iowa, and Tirpitz had more systemic redundancy in its crucial components (for example, main fire control could be commanded from 3 points, 2 of which armored - in Iowa there were 2 such points; the main turrets were 4 - compared to Iowa's 3, etc).
As the electronic equipment was comparable, so was ship tracking, fall of shot spoting and weapons response time. Thus, the probability of an early hit was comparable. However, repeated, consistent hits
would be more likely scored by Tirpitz, as hes guns could deliver over 3 shells/minute at 18000y, while Iowa's couldn't deliver more than 2,2 - 2,3. The time of flight of the German shells was smaller, and so was the time needed for aaccurate ranging. ALso, given the tight salvo patters of the 4 x 2 - 38cm gun turrets, the probability of 2 shells from the same salvo hiting the Iowa was greater than the reverse.
Thus, I would see the Tirpitz firing 4 gun salvos for the first 2-3 minutes, while Iowa would be firing 3-gun salvos for ranging. Iowa would straddle first, because it would have 3 individual brackets. However, Tirpitz would score the first hit, becase the danger space of the 38cm shells was greater than in the case of the 40,6cm shells, and the salvos were more tightly packed around the computer-plotted firing solution. After the first observed hit, Tirpitz's captain would order continous rapid fire from all 4 turrets. Iowa would also score several heavy hits, destroying or knocking -out many parts above the panzer deck; however, in 10-15 minutes of battle, at least one of the secondary magazines of Iowa would be hit by 38cm shells, and explode, causing the knocking-out of many on-board systems. Tirptiz's superior rate of fire and faster shell flight woudl slowly take its toll, and Iowa woudl be hit more times than Tirpitz. After about 20 minutes, both ships would be heavil damaged, but Iowa would get the shorter end of the stick, with all sections above the waterline being put out of action, including the command-decks. Also, severe flooding would be recorded in the bow of the ship. The top speed woudl be around 15-18kts. The main turrets woudl be on local control, firing wildly. Tirpitz would be on fire, with maybe 2 main turrets operational At least 2 hits below the armor belt would be recorded, with damage to the stearing gear and 1 turbine-room completely flooded. However, 1 command post would still be active (maybe the aft con tower ?) and accurately direct fire based on the readings of the local-turret directors and plotting of the still-operational plotting rooms (as the main directors and radars would have been previously destroyed).
At this point, both commanders would decide to retreat their badly-damaged ships. Slowly, their range would open, and Tirpitz woudl try to go for Norway.
Iowa's speed would decrease to about 10kts, and it woudl have to be towed back to port repairs would last 1-1,5 years; Tirptiz would get back on its own power and would stay 1 year for repairs. About 1000 casualties on the Iowa and 600-700 on the Tirpitz...