Builder:
I agree with KennyV on two out of three points.
I have never used an AC belt drive mower, but I have seen them run on a neighbor's place and they are very smooth.
The JD 350 is a very solid mower made in the tradition of 1950's farm equipment. I know because I have one. Just last weekend I severed both sides of a 1/4" welded chain link (don't ask how I managed to do that) with no harm except a broken section that I replaced in about 10 minutes for $2.00.
I keep up with JD 350 prices because I want a second one, and in this area (southeast US) you can't find a decent one for under $1,500 unless the seller does not know the market. They typically go for $1,500 to $2,000 around here, and that's for one that has been used quite a bit. This is not a heavy hay area, and they are fairly scarce around here. The prices may well be much lower where they are plentiful.
The JD wobble box is similar to the IH. The NH and Ford use a different type drive.
Parts are readily available from the local JD dealer, and the prices are fairly reasonable, at least in comparison to parts for my JD crawler.
I wanted a New Holland 450/451 because the drive head is simpler than the JD 350, it is still in production (by Rowse I think), and I figured it would be easier to make any parts that were no longer available. However, now that I have used the JD 350, I am satisfied that with reasonable care it will last a very long time. I plan to replace the drive head wear parts (bearings and seals) with new JD stuff, and I don't doubt that my grandchildren will be using it.
There are two limits on the angles at which the JD 350 will operate. First, the drive head (and bar that is attached to it) can only pivot until it strikes the yoke that holds it. But that is from 45 deg to the left (of the tractor) through vertical through horizontal and down to at least 30 deg (that's as far as I have tried it). The more practical limit is the mechanism that makes the drive head pivot. It is a chain attached to an arm about 8" long that sticks out of the top of the drive head. When the chain is tightened the bar pivots up, but the original mechanism only tightens the chain about 5", which is only enough to raise the outer end of the bar about three feet. To get more lift, one needs something that will pull the arm further than the chain does. One method is to replace the chain with a hydraulic cylinder. The mower in the ad you posted has been modified in that fashion. The cylinder is attached between the bar on the drive head and the mower frame. When the cylinder retracts, it pulls the bar and the blade pivots up. It is hard to tell from the picture, but I don't think that cylinder will hold the bar in the vertical position because the pivoting linkage at each end of the cylinder will not put a resisting force on the bar when it gets vertical and then starts to pivot down over the mower frame. But you could easily modify the arrangement to make it hold the bar vertical.
Good luck in your search.