Hi Jeff,
Go with either of the hydrated lime products you linked. Same price, your choice.
Where did you see that Type S mortar is acceptable? That may be from another part of the instructions (for example, when building the hearth frame from standard bricks, the high heat mortar mix is preferred, but if you just don’t have enough of that, it is acceptable to use Type S mortar in its place…we’d really rather you use the high heat mix in Steps 2 through 4 because the bricks come in contact with the hot hearth firebrick and Type S will eventually degrade in those areas).
As an ingredient for the high heat mortar mix, Type S mortar mix is not an acceptable substitute for hydrated lime, and overall its uses should be confined to these areas:
- concrete blocks for the base
- the “bed” for your two piece slab, and the joint between them
- the stucco shell over your barrel arch and insulation (Type S may be used in place of special-purpose stucco mix)
Go get your hydrated lime, and save the Type S for the areas I listed. And please, keep asking questions as you go along—this is a process, and there are no dumb questions when it comes to learning something new.
Good luck!