I think the biggest issue that you have is your budget! Now hear me out..... with that kind of money, you will be buying way more mower than you need if you get even close to the top of your budget. This forum is filled with people who will tell you how to spend your money, but what you need to decide is how much do you want to invest in something that is tasked with one job, and then to consider that at a point, no extra amount of money will do that job any better. What I am saying is that from $10k-15k you will probably see no difference in how your lawn looks or how fast it gets cut. First, your deck size is only as important as your ability to utilize that deck on your property. Since you have the embankment and some landscaping already, you can pick a deck that will get everywhere that you need it to get without being too wide to hit things, scalp on uneven patches or dig in at the bottom of your embankment. Then you have to consider the features that you want. A good seat is important if you are going to be sitting in it for a while. Your ground doesn't look too bad so I would look for a good adjustable seat before a full-framed suspension system like on the Ferris (although this does not discount them in your choice). Lastly, you should be looking at the total package including value (what you get for what you pay), dealer support (because you will need them), warranty (because we all like peace of mind) and cut quality (because this is what the machine is meant to do).
And to now debunk a few "myths," a fast mower doesn't cut grass fast, it simply drives fast. I don't know of many people with ZTR's that can cut at full speed either because grass conditions do not allow for it or the skill necessary to cut nice straight lines, or like on your lot, curved lines is not easy for a lot of people, even with experience. Also, buying an expensive mower doesn't guarantee longevity. Yes, higher end components in these machines will have more trouble free hours of use, but maintenance on these machines is just as important as any other machine, and possibly more important. This is where having an intimate knowledge of your operators manual is very important.
Now for what I think that you should do, because at the end of the day, that is what we do here, we try to spend your money for you!!! I am a big fan of Exmark, but also like Scag and Ferris. I have owned two Exmarks and the cut quality of both has been exceptional. The older one I had did take some maintenance and at about 12 years old I had started to put some money into it to replace parts that had worn. I think it was around 500 hours when the PTO clutch went, as well as the spindle bearings, caster bearings/races and the gaskets around the bottom end of the engine. I put about $700 into it at that point and it was running like new again. My newer Exmark was, well new, so it did not have any problems when I sold it (I sold it because I want to get a garden tractor). As for Ferris, my step-dad has one and he loves it. His has a 61" deck, 28hp Vanguard EFI, marbain blades, full frame suspension, nice wide tires for traction and minimal rutting. This machine is a beast. It is 3 years old now and his only issue was a leaking hydrostatic which was covered under warranty. Other than that is can cut through 10" tall grass throwing it out 4-5 feet and not miss a blade of grass beneath the deck. Lastly for the Scag. I have shopped and talked to people who have owned these and they are well built machines; just ask contractors who use them.
Looking at your yard, and considering your budget, I recommend the following three mowers:
1) Exmark Lazer Z E 52"
2) Ferris F160Z 52" or IS2100Z 52", either with the 810cc Briggs Vanguard
3) Scag Tiger Cat II 52" with the Kawasaki EFI
All of these mowers are right around $10k, saving you a big chunk of change. I placed them in this order because from my experience the Exmark is going to leave the nicest cut, the Ferris has the best engine and the Scag will offer good cut quality and good value for the money.
REMINDER: This is just my opinion and to be honest, I wouldn't mind being in your position right now!