I think, Brian, you are confusing the Ektenne form with the Bidding Prayer. The Bidding Prayer is the classic Western form that sadly early disappeared from the mass save for on Good Friday. But in it, the deacon did indeed bid facing the people (and they were also told to kneel as they silently prayed for the bid, then to stand again when the priest prayed the collect). But the Ektenne form does not involve any turning at all. It is prayed toward the altar entirely.
I was taught, back in the connected-to-the-wall altar, that when speaking to the congregation we faced them. When the words are addressed to God, we faced the altar/wall. "For …, let us pray." is addressed to the people. "Lord, have mercy," is addressed to God.
Good Friday Bidding Prayers (which I normally used,) had an assistant speak the invitation to the congregation while facing them. I kept facing the altar during the invitation.
I once asked Paul Nelson when he was the head of the ELCA Worship about the petitions in
Sundays and Seasons. Sometimes they were prayers addressed to God. Sometimes they were invitations to the congregation to pray. He said that the problem with the invitations is that they should be followed by a period of silence for prayer before the concluding, "Lord, in your mercy, hear our prayer." The silence for prayers seldom happened.
For most of a latter days of ministry, there was a free-standing altar. Invitations and prayers were said behind it while facing the congregation. An added benefit, that another pastor just mentioned at lunch yesterday, is that a lot of people watch the speakers' mouth to help them understand what is being said. (I found that also true with singers being in front of the congregation rather than behind them.) Seeing the lips of a speaker helps people hear.