I can’t speak to the oil tank placement, but I can relay some first-hand experience about option B.
Last year we housed our 2X6 in a “Garage in a box” that we got from Tractor Supply. Nothing more than an aluminum frame with a fitted tarp over it. It was open on both ends and had a roof and side walls, very similar to your wood shed, as I picture it. We stuck the stack out just far enough from under the tarp to keep it from melting. The arch was up on blocks, just as you describe.
Here are the downsides:
The steam will condense on the underside of the roof and it will rain under there, on you, back in your pans (carrying with it anything that was once above), and on everything left out and uncovered.
Water everywhere, snow run off, rain, condensation, etc. caused the area around the arch to become a muddy mess. We bought some indoor/outdoor carpet to put down near the arch to keep the mud to a minimum.
With the aforementioned, keeping the wood dry presented its own challenge. Never thought I would have to put a tarp over wood that was under a roof.
The slightest breeze will cause the steam to swirl under your roof. If you are a wearer of glasses, as I am, this resulted in instantly fogged glasses, and usually at the worst possible time, like a draw.
A strong wind would rip right through your cold and soaked clothing, even on a bright sunny day. I had to wear rain gear at all times.
I’ve had more miserable experiences, but I can’t remember when.
42.67N 84.02W
350 taps- 300 on vacuum, 50 buckets
JD gator 625i Sap hauler w/65 gal tank
Leader 2X6 drop flue
Homemade auto draw-off
Homemade preheater
Homebrew RO, 2- xle-4040's
LaPierre double vertical releaser
Kinney KC-8 vacuum pump
12X24 shack
Lots of chickens and a few cats.