Argument from Passover
The Last Supper was the Passover meal, which required the eating of unleavened bread:
Luke 22:7,8 (ESV)
Then came the day of Unleavened Bread, on which the Passover lamb had
to be sacrificed. So Jesus sent Peter and John, saying, “Go and
prepare the Passover for us, that we may eat it.”
Exodus 12 and 13 prescribe a week of eating unleavened bread with the Passover meal at the end.
This suggests the meal in Emmaus was with leavened bread rather than the unleavened bread prescribed for the holy week of Passover, because it takes place several days after the Passover week was completed. This argues against reenactment, although not conclusively.
There are other occasions in which Jesus broke bread with the disciples. One notable example recorded for us is Matthew 4:19 (Jesus Feeds the Five Thousand).
Then he ordered the crowds to sit down on the grass, and taking the
five loaves and the two fish, he looked up to heaven and said a
blessing. Then he broke the loaves and gave them to the disciples, and
the disciples gave them to the crowds.
This suggests it was customary for Jesus to say a blessing at the breaking of bread (not just unleavened bread) and is similar to the meal in Emmaus:
Luke 24:30 (ESV)
When he was at table with them, he took the bread and blessed and
broke it and gave it to them.
In this view, it is the combination of blessing and breaking bread which caused the men to recognize Jesus, not necessarily a Passover reenactment.
Argument from Disfiguration
This is another line of reasoning which seems sound (and a bit romantic, too!), though some might think it is grasping.
These disciples did not recognize Jesus at first, and the question is, why?
The answer given is that Jesus was disfigured. Scripture support is offered as follows:
Isaiah 50:6 (ESV)
I gave my back to those who strike,
and my cheeks to those who pull out the beard;
I hid not my face
from disgrace and spitting.
Isaiah 52:13-15 (ESV)
Behold, my servant shall act wisely;
he shall be high and lifted up,
and shall be exalted.
As many were astonished at you—
his appearance was so marred, beyond human semblance,
and his form beyond that of the children of mankind—
so shall he sprinkle many nations;
kings shall shut their mouths because of him;
If these passages can be taken as Messianic prophecies (there is especially good evidence for the second one), then it can be extrapolated that the beating Jesus took left him disfigured beyond recognition (he had his beard pulled out, was marred beyond human semblance).
Compare these to Luke 22:63,64; Mark 15:19; Matthew 26:67,68
This can explain why Mary didn't recognize him (in the same way as the men at Emmaus).
John 20:17 (ESV)
Having said this, she turned around and saw Jesus standing, but she
did not know that it was Jesus.
The reason they may have recognized him in the breaking of bread is the revelation of his scars when he raised his hands to bless the bread. This would have been a telltale sign. The nail prints would have functioned the same way they did for (doubting) Thomas:
John 20:27,28 (ESV)
Then he said to Thomas, “Put your finger here, and see my hands; and
put out your hand, and place it in my side. Do not disbelieve, but
believe.” Thomas answered him, “My Lord and my God!”
But at least a couple other reasons why Jesus could have been "known to them in the breaking of the bread."