Hello Anna,
It is very difficult to give an opinion of a pistol based on images and without an inhand inspection, so I shall do the best I can based on your description and images. If you do not mind, I would like to give you my opinion of this particular pistol.
In my opinion, the engraving on the chamber is NOT factory engraved and, therefore, this leads me to feel that the pistol has been refinished after the engraving. The engraving is crude for a 'presentation' pistol, so this gives me bad vibes about this pistol. A presentation Luger from the DWM factory would definitely have a better polished finished than compared to what I see on this pistol. I have examined a few presentation Lugers in my hands including the M1902 'GL' HCR presentation carbine (see image hereunder) which was a gift from Mr. R. J. Reynolds of the Reynolds Tobacco Company to his Chief Financial Officer Mr. Harold Conwell Roan in 1903. His name is listed the the book entitled 'The Golden Leaf'.
When I carefully examine the condition on a Luger pistol, I look for CONSISTENCY. If this pistol would have retained 99% original factory finish, there would have been a high percentage of straw on the safety lever. The safety lever on this pistol has hardly any straw remaining and it is nearly smooth - there is no so-called 'tiger-grain' machine marks on the lever and these characteristics must be present, especially on a near mint pistol.
Furthermore, when I look at the various images, I do not notice any patina on the pistol. Every pistol made before 1945 WILL have some presence of micro patina no matter the amount of care given to the pistol.
You can accept or reject my opinion, and I apologize if I may have upset you. If you want to receive an accurate opinion, may I suggest that you make arrangements to allow Ron Wood to examine this pistol in his hands.
By the way, I like your Ideal rig which looks correct based on the images.
Albert