Did N Ough draw plans of Tiger? I can't recall them if he did.
The battlecruisers rudders, such as the 'cats', had a total of 70 degrees of throw ... 35 degrees each side.
So far I'm finding that an image of her 24in twin searchlights are really hard to find. I'm looking for them on others ships of that era for my own 'big cat' and what complicates matters is there was at least 3 versions of the twin 24in mount (no doubt each by a different manufacturer). Lion class & Tigers may be the same?
I will fit and wire nav lights, but I suspect from my reading that she would never had shown lights while in this configuration; True or false?She'll have had the red & green navigation lights on a bridge platform. She'll have had white lights on the mast(s) and somewhere on the rear structure facing aft will have been 3 lamps arranged horizontally, such as: x.....x.....x
I don't now their colour nor their purpose [maybe positional for the next astern?] but have seen them on several classes of capital ship. I did look through what images I have of Tiger but can't see them on her so I've included images of the first 4 ships I found that show them clearly. I marked Courageous's with blue to make them clearer.
Any interior 'fighting lamps' were blue shaded.
Re: the 'conning tower'. Don't wish to
'teach granny to suck eggs' but the armoured hood for the argo rangefinder sat on a "squat spotting tower some 3ft 9in high and 9ft internal diameter" on the roof of the conning tower. The additions either side of the conning tower are the control positions for the secondary armament. The main-armament 'Director' was on the roof of the 'spotting top'.
am unsure of some of the detail, eg around the conning tower which I think is incorrect.The only thing I see missing on the conning tower is the vision slit under the flat roof. Plus the roof fittings you mentioned you still needed to add.
p.s. in the photos which one are you? Don't say the good-looking one!

p.p.s. may be able to help with the main derrick rigging scheme. I will look into it. That for the small boats should be easy to transfer over from the shorter radial davit. IIRC, Tiger has high davits.