Does the middle voice of τιμάω (τιμάομαι) in Attic Greek usually have an active (i.e. Epic: “to avenge”) or a mid/passive meaning (“to be honored”)?

Perusing the entry for τιμάω in Liddell–Scott, the negative meaning you mention is not Epic, and first turns up in Plato and Aristophanes; LSJ describes it as an “Attic law term”. The transition is:

• to honour (since Homer)
• to award (as an honour) (in Tragedy)
• to award a penalty to someone, including a fine or a death sentence (in Attic legal contexts)
• (medial) to estimate the extent of one one’s own penalty (in Attic legal contexts)

It is a specialist meaning, and I’d expect that the main meaning, ‘to be honoured’, continued to be dominant; it certainly is the meaning you would expect in a non-legal context.