Dear Annie,
I'll take a shot, though I'm neither a priest nor a monk nor a scholar!
Ethiopia has more styles of cross than any Church or country in the world. Every province of Ethiopia (and there were 99, each ruled by a king under the Emperor) had its own style of Cross.
The most famous is the Cross of the Emperor St Lalibela with the widening ends on all four arms.
A feature on many Ethiopian Crosses (or the "Maskal") is a representation of the Tabot or Ark of the Covenant of Moses - the Ethiopians venerate the "Shekinah" or Presence of the Lord in both (which is why their "Sabbath" is two days - Saturday AND Sunday).
On Ethiopian hand crosses, there is often a little square at the base of the handle, frequently with ten dots or the like, which represents the Ark of the Covenant. Every Ethiopian parish has a wooden Ark with the Ten Commandments named for a Christian saint and it is this that is the object of veneration.
There are a lot of "X's" on Ethiopian crosses to signify the first letter of Christ's Name in Greek - the earliest form of the Cross as per Constantine or the "Chir Rho."
The Greek Style of the Cross with equal parts represents the Trinity. The middle bar is the Father and the other two "arms" represent the Son and the Holy Spirit as the "Arms" of the Father.
The intricate detailing of many of the Crosses represents the teaching of the Gospel and the many things that Christ did on earth that, if they should be written down, the whole world could not contain the books that should be produced. (Didn't one of the Evangelists say something like that?

).
(The intricate stitch patterns on the Russian Old Believer Lestovka also represents the teaching of the Gospel - and I think Diak will back me up on that one!)
The Ethiopians wear their neck cross on a "matab" which, according to my local Ethiopian priest, is a cord made of three, intertwined green, yellow and red cords.
(The Knights Templars, when they were in Ethiopia, adopted this practice, but used black, red and white cords to make one on which they wore their Knight's Cross which was, in fact, the Lalibela Cross, the Cross of the Templar Order).
There are several explanations for the Celtic Cross that I've come across.
One is that it is a Christianization of the sun-cult that was prevalent among the pagan Celts.
The Ukrainian Church also loves the Celtic "haloed" Cross for this same reason - we even have hymns in which we glorify Christ as "our Sun, Life and Paradise!" We could have received the Celtic Cross from the Celtic missionaries that had a presence in Kyiv from the time of St Olha.
Another explanation is that it is simply a form of the "Chi Rho" Cross by the Celtic missionaries.
Both forms were used together by St Ninian of Galloway and St Columba MacFelim O'Neill, of Niall Nine-Hostager!
Another explanation is a Eucharistic one where the circle is a mill-stone used to grind wheat and some missionaries used to make large crosses with the millstone fastened in the middle.
(Hopefully, I haven't misrepresented anything here to Brother Neil's chagrin!)
As for the Tau, there is the view that this is the Egyptian Cross, the Cross of St Anthony of Egypt.
Some believe that the "Ankh" which is a Tau Cross with a circle for a handle used to carry the item around is the origin of the Tau Cross.
Greek missionaries to Egypt, when they saw the Ankh symbol, used it to convert the Egyptians to Christianity by telling them that they already HONOURED the Cross of Christ Who had revealed it to him.
This was a well-known Christian missionary "trick"

.
At Chartres in France, where the cult of the Virgin Mary is VERY ancient, the Christians there saw pagan Celts worship an image of a Virgin Queen seated on a throne holding a child on her lap . . .
This is what became the image of Our Lady of Chartres.
To this day, there is a feast at Chartres in honour of Our Lady of Chartres, "circa 100 B.C." (!)
In the undercroft of the Cathedral is the original, but worn, icon of Our Lady of Chartres, not far from the restored wooden statue.
So the Tau was honoured in Egypt, but mostly in Europe, since St Anthony's time.
It could very well have been the form of the Roman cross of execution - except that evidence is strong that the favoured Roman cross was either an actual "X" cross (i.e. the Cross of St Andrew and I've heard interior decorators refer to the "X" as the "Roman cross") or else a "Y" form of the Cross (the coat of arms of the Kozak Hetman Ivan Mazeppa - there was an opera that played in the U.S. in the 19th century named for him - had a large "Y" on it representing a form of the Cross).
The thing is that since crucifixion was so prevalent as a form of execution, people took the methods used "for granted" which is why we are only now, with the help of archaeology, reconstructing what crucifixion actually was and what crosses looked like.
This is also why in the Eastern Byzantine Church, there is a rule that insists that every representation of the Cross of Christ MUST have the "IC XC" on it to indicate that it is indeed Christ's Cross - and not someone else's!
Origen and others have given some indication about what the Cross of Christ looked like - and this, truth be told, comes very close to the Orthodox Cross of Calvary.
Origen mentions the "subpedalion" or footrest that held the weight of our Lord's Sacred Body. Even Western crucifixions depict Christ's Body on the Cross inclining toward the Good Thief which would have more than likely have resulted in the footrest taking the shape it does in today's Orthodox Cross.
Origen also mentions the "title" or written out charge against Christ (only the crime of treason was punishable by crucifixion where the victim was nailed, rather than roped, to the cross).
Origen said he was in a church in Syria once that had one of the three portions of this title (divided into three earlier).
He described the wood as being light and said that Pilate had used a red crayon to write "This is Jesus, King of the Jews" on it in three languages - as he saw for himself.
Even if the Tau was the basic form of the Cross, there would have been an elevation for the display of the "Title" of Pilate for all to see.
There are, in European Christian heraldry, 285 forms of the Christian Cross. Even the Star of David is considered a form of the Cross!
Alex