There are two good options, both of which are very commonly used.
1)Reverse turn
2)Fallaway reverse turn
The reverse turn (and feather finish) is shown in the learning centre on this site.
for both these options, the lady is back in line for the first step.

#1. The Reverse/Left Turn started from a closed position presents no problem.
However the Feather step ends with the man's right foot outside partner.
A left turn from that position is possible and I have been doing that but it is not smooth, actually awkward.

#2. Fallaway reverse turn
I don't know exactly what that is.
I have used a hover after featherstep
but that means the woman has to change from contra body to promenade position
which is also very awkward.

Dont get alarmed-- natural turns traditionally seem to present more of a challenge than Rev.
The Falaway, is a much more advanced type of figure, and there are several more that you need to add to your reportoire before that .

You seem to speak like a beginner-- add for e.g. ( in FT ) Impetus turn.and natural weave--2 nice figures that are more within you level .

Gudway. I believe that what you called a Hover is actually an Open Telemark which finishes in a Promenade Position.It is only awkward if you both open too soon and too wide ,especially the lady. With the lady they see where they want to go and stop turning. They should continue turning and finish looking at the outside of their hand and not looking through the middle. I hope that is not too difficult to understand. Good luck

If you both open ?-- I hope its only the lady creating the postion .

"However the Feather step ends with the man's right foot outside partner.
A left turn from that position is possible and I have been doing that but it is not smooth, actually awkward."

It is considered to be the height of smooth elegance by those who have learned to dance it well.

However, the outside partner position, especially if it occurs on a third step, is a fairly challenging one.

This particular combination of positions is absolutely classic. However, if your use of the word 'smooth' implies the american smooth style, it is worth pointing out that a literal feather step is not considered a basic element there, though variations of the feather such a feather commenced in promenade position (which would still get you to this position on 3) are core parts of traditional usage.

Anonymouse. Oh boy here we go. Todays dancer if you care to watch, there is plenty to watch on youtube, The second step of the Reverse Turn in the International Style Foxtrot is a step to the side being up on both toes. This will allow the lady to complete her heel turn. If you intend to do an open turn where the lady does not do a heel turn and is stepping outside the partner. Then that second step for the man will go to a different place. If it is not comfortable it is not right. Words spoken by Len Scrivener.

"Anonymouse. Oh boy here we go. Todays dancer if you care to watch, there is plenty to watch on youtube, The second step of the Reverse Turn in the International Style Foxtrot is a step to the side being up on both toes."

The heels are raised and not contacting the floor, yes, but this is the moderate rise of foxtrot, not the extreme rise of waltz. In many of these cases the rise is limited to the degree that when the lady does the comparable action, the higher heel of her shoe actually is on the floor, and described that way in the technique book.

"This will allow the lady to complete her heel turn."

A heel turn requires a bracing action in the legs, it does not actually require much in the way of foot rise at all, though it takes a year or more of experience to be able to lead a heel turn reliably without also putting in moderate foot rise. Now of course there is foot rise in the basic foxtrot reverse, but there isn't waltz quantity foot rise. The heel turn comes from the braced leg (knee stays relatively straight as you arrive on the foot, not bending deeply as it does in waltz), not the foot rise.

The key point is that the foot rise for a well timed foxtrot must be moderate enough that both dancer's have the ability to sustain the resulting downswing from that height. Rise to high, and they can't do this, meaning they will rush the step after the lowering as they are unable to draw it out into a full movement.

Obviously, the amount of foot rise that a top professional you might see on a video can safely use without breaking the flow of their movement is going to be much more than what an intermediate dancer can use. But the amount of foot rise a skilled professional uses in a characteristic foxtrot movement will also be much LESS than the amount they use in waltz, because foxtrot has a fundamentally different character of movement - a character that is about movement across the floor much more than rise and fall above it.

So. First step Reverse Turn Foxtrot for the man Foot Rise. For the lady no foot rise. Its been that way since 1920. Pages 175 to 178.
I would suggest that you find one of those top flight professionals . Go frame by frame and see exactly how much the knee bends on step three of the Feather and step one of the Reverse. Don't assume, go look. I am looking at Timothy Howson in the 06 final at Blackpool.
The Foxtrot has to be exact technique wise. We can get away with murder in the other dances but not in the Foxtrot. Anybody can learn the steps. But when you hear that this is the hardest dance to do that is what they are referring to.

"So. First step Reverse Turn Foxtrot for the man Foot Rise. For the lady no foot rise. Its been that way since 1920. Pages 175 to 178."

No one disputed this. The issues is that the foot rise used in the situations is MUCH LESS than that used in waltz, because foxtrot does not have waltz rise. If someone dances it with waltz rise, they will not only loose the foxtrot character, they will also have a hard time achieving the desired character because the energy gained from descding from a waltz altitude will overpower their following slow - causing them to rush that step, and then rise too high to absorb the excess of energy. It becomes a vicious cycle of too high - too soon - too high.

"I would suggest that you find one of those top flight professionals . Go frame by frame and see exactly how much the knee bends on step three of the Feather and step one of the Reverse."

Substantially less for a heel turn than for a waltz-type turn. The follower's heel turn is created by arrival onto a largely straight leg - it is this "standing up" that establishes the "on the spot" axis of the turn, and failure to create it is the usual cause of failed heel turns. Of course you can do a heel turn with bent knees - the leader's heel turns are all done that way, but it is improper for the follower to do this as it would then be missing the essential characteristic of a followers heel turn - up, being rotated by partner, instead of down, rotating the partnership as the leader would dance it.