Sea Breeze:
To "worship" in Koine Greek (and in ancient times) means to "offer an act of obeisance" in modern American and UK usage.
The word at Hebrews 1:6 is the Greek verb PROSKUNEO, and it means to "perform an act of reverence before" another person, usually one of higher rank or someone you honor.
It occurs, for instance, at Matthew 20:20:
Then the mother of the sons of Zebedee came to him with her sons, and kneeling [proskynousa] before him, she asked a favor of him.
According to Josephus, this was the way people would greet the high priest--he actually uses the same Greek word--since they were the representative (though not the incarnation of) God, during the days the Second Temple was standing.
This likely explains why Cornelius is spoken of greeting Peter at Acts 10:25, with the use of the word PROSKUNEO and Peter rejects it.
To show that the word has only reference to the act and not to creed (which is often the case in Judaism), it is used in John 4:22) as the word for "worship":
You worship what you do not know; we worship what we know, for salvation is from the Jews.
One can "worship" what they "do not know." In other words, one can "bow before" something they have no real knowledge of.
If the word meant to "worship" as in "belief and adore and creed," then that would be different, but PROSKUNEO does not. It refers to homage, kneeling, prostration.
Jehovah's Witnesses do tend to bend the rules a lot with the New World Translation. But in some cases they are just different, in the minority--and people find it irksome.
In the end, it is a play on words. Obeisance is something you give to a king or a deity anyway, and a king almost always represents a god on earth. Again just like the high priest of the Temple was a representative of God (though not an incarnation). So it doesn't matter what word you use. The context still states in Hebrews that Jesus is greater than the angels because he is like God to them.
And thus the problem with whatever words the NWT tries to choose. You can only go so far.