250 hours is a lot of time!
I have a friend that is in his late twenties and is now a partner for a boutique investment shop. About four years ago he made a commitment to pass the CFA 1 in nine months. Studied a little each day after work, and then studied more on the weekends. 180 hours total. Passed the CFA 1 without any fan fare. Hardly told a soul. Did the same for the CFA 2 the following year. Didn't tell any colleagues. No fan fare. Boss was pleasantly surprised when he listed the new qualification on the firm website.
He does the exact same thing the following year for the CFA 3. His wife tells someone at the firm, and when he walks into work they throw a surprise celebration for this very impressive accomplishment (many people spend a decade reaching CFA 3).
A couple months later the managing director moves to have the firm make him a partner. Easy decision. You had a junior analyst quietly dedicate themselves to substantially improving their skills.
Now, while his salary is certainly quite impressive as a partner and for someone that young, the true freedom he has achieved is being given responsibility of a new order of magnitude to establish things he wants to establish in that world (internal values maybe, many new types of clients, new employees he can then bring up through the firm, etc.).
Point is: good on you. You're a lesson for most of us.
You ask for 6 weeks unpaid leave. Could be one block, or 1 day a week for 30 weeks. This will cost you $10k gross by my calculations.
Even if you get the $100k job, you are $10k up after 1 year, with no friends and family time sacrificed at all.
As a bonus you were effectively paid for 6 weeks to learn CS skills rather than bash out features and not learn any new computer science skills.
Just FYI - this interview process isn't a one and done thing. You have to refresh yourself at least every year with ~80 hours of prep. Otherwise, you're going to be really bad at it when you search again.