"Touch me not, for I have not yet ascended to my Father in Heaven", could be interpreted more as "Don't worry, I'm not going leaving for Heaven just yet. You don't have to cling to me like that."

There is evidence that Jesus ascended to heaven twice, but this evidence does not come out of John's Gospel but out of Luke/Acts.

First of all, Luke 24:13 tells us that what follows occurred on the same day as the resurrection:

And, behold, two of them went that same day to a village called Emmaus, which was from Jerusalem about threescore furlongs.

Then, Luke 24:33-36 tells us that the two returned to Jerusalem and that Jesus appeared to them the same evening:

And they rose up the same hour, and returned to Jerusalem, and found the eleven gathered together, and them that were with them, And they told what things were done in the way, and how he was known of them in breaking of bread. And as they thus spake, Jesus himself stood in the midst of them, and saith unto them, Peace be unto you.

And the same evening, Jesus took the disciples towards Bethany, where he was lifted up to heaven:

And he led them out as far as to Bethany, and he lifted up his hands, and blessed them. And it came to pass, while he blessed them, he was parted from them, and carried up into heaven.

Another, more famous occasion occurs after forty days, near the mount of Olivet (Acts 1:3,9):

Acts 1:3: To whom also he shewed himself alive after his passion by many infallible proofs, being seen of them forty days, and speaking of the things pertaining to the kingdom of God:

Acts 1:9: And when he had spoken these things, while they beheld, he was taken up; and a cloud received him out of their sight.

Only the author of Luke/Acts writes of Jesus being taken up bodily to heaven in the sight of the disciples (The 'Long Ending' of Mark was written later and briefly follows the lead of Luke). The first occasion, in Luke's Gospel, was on the day of his resurrection. When writing Acts, he may have wished to bring the Jewish festival of the Pentecost into his story, and so wrote of the ascension after forty days and then the Pentecost on the fiftieth day.

IMO Jesus ascended after talking with Mary and before meeting the brothers in Galilee.

The whole picture of the sacrifices and offerings and the feasts days in the OT are a picture of the Messiah.

During the Passover week (days of Unleavened Bread) the Lord told the Jews to do this. After sunset ending the regular Sat. sabbath the High Priest went to the field and cut enough barley to make an omer (1/10 of an ephah) for an offering to the God of the firstfruits of the harvest. This was called the 'Wave Offering'. Very early the next morning on the first day of the week they beat the barley grain off the stalk and cleaned it of chaff, purifying it. Then the High Priest lifted up the bowl containing the omer of barley and brought back down. Jesus was the Firstfruits of the Resurrection. I believe that as the High Priest cut the stalks loose from the ground Jesus was Resurrected shortly after sunset on the Sat. sabbath which would have been the beginning of the first day of the week for the Jews. Then Mary sees Him. "say to them, I ascend to My Father". As the High Priest lifted up the omer of barley as a firstfruits offering, Jesus ascended to His Father as the Firstfruits offering of the Resurrection.

In the passage in John 20:17, the word used for Touch ἅπτομαι, is not used in John 20:27. This word is used in different ways throughout the bible.

This means that it is not unreasonable for the passage to have meant "to hold on to" or "grasp".

Some eisegesis here, but if a person had a loved one they presumed to be dead, and they find them alive. What would they do? I would embrace them in excitement.

Now this is speculation, but we do know that Jesus wanted Mary Magdalene to not touch him (embrace) and instead wanted her to tell His disciples the news.

The passage never explicitly states that she did not touch him either, but the next verse makes it reasonable to believe that she did not since it says that Mary saw Jesus.

Furthermore

I ascend unto my Father, and your Father; and to my God, and your God

There seems to be the assumption that this means Jesus ascended into heaven at that very moment, which doesn't seem to be apparent to me.

Also, look at other translations

Many translate ἅπτομαι as hold.