I don’t particularly understand the question. When using the specialist specialties you simply have 12 days to work with in a single session instead of the usual 10. This does not change anything else about the profession.
If I have “Wood Specialist” when putting planning out my Hard Action for a session I could do things like:
Example 1 Not using only Wood
- 8 Days & 16 Basic Metal: Build a Break Two Handed Melee Weapon
- 2 Days: Collect Materials
Example 2 Not using only Wood
- 8 Days, 15 Basic Metal, and 1 Special Metal: Build a Break Two Handed Melee Weapon with an unknown extra effect on it.
- 2 Days: Collect Materials
Example 3 Not using only Wood
- 8 Days & 16 Basic Metal: Build a Break Two Handed Melee Weapon
- 2 Days & 4 Basic Fiber: Build a Trip Dagger
Example 4 Using only Wood
- 8 Days & 16 Basic Wood: Build a Maim Two Handed Melee Weapon
- 4 Days: Collect Materials
Example 5 Using only Wood
- 8 Days & 16 Basic Wood: Build a Maim Two Handed Melee Weapon
- 4 Days & 8 Basic Wood: Build a Crushing Dagger
Example 6 Using only Wood
- 8 Days, 15 Basic Wood, and 1 Special Wood: Build a Maim Two Handed Melee Weapon with an unknown extra effect on it.
- 2 Days, 3 Basic Wood, and 1 Special Wood: Build a Stun Crossbow with an unknown extra effect.
- 2 Days, 3 Basic Wood, and 1 Special Wood: Build a Stun Crossbow with an unknown extra effect.
You can not just “spend” extra days on building something, doing so would yield no extra results.