My question is this: If I were to enchant my own creature with this, could I sacrifice multiple permanents to the ability in the same turn?
Only if you get priority in the cleanup step, after the "ignore this effect" has expired.
Quote:
115. Special Actions
115.1. Special actions are actions a player may take when they have priority that don’t use the stack.
These are not to be confused with turn-based actions and state-based actions, which the game
generates automatically. (See rule 703, “Turn-Based Actions,” and rule 704, “State-Based
Actions.”)
115.2. There are eight special actions:
115.2d Some effects from static abilities allow a player to take an action to ignore the effect from
that ability for a duration. Doing so is a special action. A player can take such an action any
time they have priority.
Ignoring the effect of that ability means ignoring the
entire effect, including the special action to ignore it.