Here is the deal. I want to install a target classic or buffalo hunter barrel on my H&R Ultra in 308. I want to mount my old Unertl [10x] scope on it and use it for fun shooting and hog hunting.

Can I still get the 38/55 or am I limited to the 45-70, and will it install on my Ultra Hunter action?

The 45-70 BC and 38-55 Target barrels will work on the Ultra frame which is the same SB2 frame that comes on the Handi and the Classics, but the 38-55 is no longer made, it was discontinued in early 2008, last accessory barrels were sold in 2008, so you're looking for a second hand barrel or possibly old inventory somewhere. 45-70 BC barrel is still available as an accessory barrel, pending stock availability of course.