I use the Forster reamer. Ebay has one currently listed (that I found, may be more) and you can put together an entire .45 set for under $50 if you shop around.
The taper you mention may or may not be an issue during reaming or neck turning, only experience will tell.
The .244 Remington case is exactly the same as the 6mm. Remington set the twist on the .244 for light bullets, but the .243 Winchester zoomed into popularity as a deer gun with it's twist perfect for the 100 grain pills, so the niche-caliber .244 languished.
Wanting to overcome market resistance brought by the .244 mess, they re-introduced the caliber as the 6mm, selling rifles with a heavier bullet twist rate. Never came close to the .243. I have a 788 in 6mm and it's a tack driver, awesome rifle for the $110 with scope and mount I paid in 73 or 74.
You should try the forming without annealing first. Go in stages, .010 to .015 thousandths larger at a time. Brass is often pretty workable as is.