[X] This is Dawongr Weber's money. The funds will largely go projects within the Karaz Ankor - your tower for one, but also investing in the Undumgi or Ulrikadrin, or purchasing goods made by Dwarven artisans or sold in the markets of Barak Varr.
I think that this is the most appropriate loophole for us. If we want an amazing tower, we'll need to spend an amazing amount of money to properly set it up. Fortunately, we have an amazing amount of money, and the money will be going back to Karak-Eight-Peaks for them to use to continue the reconquest. You scratch my back, I'll scratch yours.
[X] Karag Nar penthouse
The first possibility that leaps to mind is the uppermost dwelling of Karag Nar, with a beautiful 360-degree view and a commanding position. The Black Orc Warboss' reasons for taking it for his own are obvious, and though it will take some time and effort to clear out the possessions that hadn't been safely stowed in the King's Armoury, it is bursting with potential and would allow you to keep a careful eye on the Undumgi and Death Pass.
[X] The Grand Abyss
If you value secrecy over all else, you could go just as far down as you can up. Deep below Karag Lhune lies the Lhune Deeps, and below that is the Grand Abyss. The Dwarves never were able to plumb the extent of its depths, and that is somewhat concerning, but it would certainly be impressive to have a tower built atop a bottomless pit.
I like both of these options really. The Karag Nar penthouse has the description of bursting with potential, and the image of a large tower being built atop the peak of Karag Nar for all to see amuses me. Especially since we are of the Grey Order. The Grand Abyss also appeals to me, given that we have stuff we would really like to keep secret. As such, absolute secrecy would really help us there. Also, having a tower built on top of a bottomless pit amuses me.
[X] Convince Esbern and Seija to stay long enough to deal with the spiders in the Chiselwards.
This suggests a future assisting Karak Eight Peaks with its reconquest, as a Spymaster focused on threats within the Karak.
[X] You're going to have a rough time explaining your windfall to the Bursars. Better to get that over with.
This suggests a future performing an assignment the Grey Order thinks is suited to you.
[X] Write a series of papers on the magical phenomena you witnessed. Or better yet, get your Journeymanlings to do the actual writing.
This suggests a future of investigation and study at Karak Eight Peaks, and perhaps helping Johann poke at Skaven technology.
I like all three of these options, to be honest. I like Karak-Eight-Peaks, and want to help it continue the reconquest, but I also want to start working on building our reputation with the Grey Order to start becoming a mover and shaker in the Empire as well as Karak-Eight-Peaks. I also think that writing a series of papers of the stuff we witnessed will keep us around Karak-Eight-Peaks, but also start getting favor with the Colleges. Also, the research option has some good synergy with convincing Esbern and Seija to stay around. More Journeyman to write the papers for us!