!ask Tail-Cloaked Matriarch says "Play it to your base, ignoring its cost." The unit I bring back (Sneaky Deckhand) has "You may play me to an open battlefield." Does the unit's own destination permission override Matriarch's directed "to your base," or is base forced? Cite the rule please.

No — base is forced. Sneaky Deckhand enters at your base even if an open battlefield exists.

Matriarch's Empower trigger is a Limited Play Effect (Rule 419.3). Per 419.3.b, the play follows the normal steps "except as noted by the game effect creating this Limited Play Effect" — and the effect explicitly notes the destination: "Play it to your base." Sneaky Deckhand's own "You may play me to an open battlefield" only expands the valid locations when it's played normally; it can't override a destination already fixed by the effect that's performing the play (same reasoning as the FAQ ruling on Shen, Kinkou summoned by Matriarch — he also lands at base).

Note: "ignoring its cost" still applies, and it's still a play — so if you want the Conquer trigger, you'd need to move him later, because he doesn't contest an open battlefield from your base.