The assumptions behind your question are based on two false premises.
First, the meaning of the words Jesus spoke to Mary and to Thomas eight days later is not the same. Jesus said to Mary,
Do not hold on to me,
whereas the words he spoke to Thomas were
Reach here with your finger . . . and your hand . . . [and touch the wounds in my hands and side]
There is a big difference between the words hold on to and touch (or technically, "put your hand in my side").
Quite naturally, I suggest, upon seeing Jesus that resurrection morning, Mary in her exuberant joy wanted Jesus to stay on earth forever, hence her "holding on to" Jesus. As for his ascending to the Father, Jesus could very well have been referring prophetically to the ascension documented in Acts Chapter 1:
And after He had said these things, He was lifted up while they were looking on, and a cloud received Him out of their sight. And as they were gazing intently into [h]the sky while He was going, behold, two men in white clothing stood beside them. They also said, “Men of Galilee, why do you stand looking into [i]the sky? This Jesus, who has been taken up from you into heaven, will come in just the same way as you have watched Him go into heaven” (verses 9-11, NASB).
Thomas, on the other hand, unlike Mary, did not really believe Jesus had risen from the dead. He, unlike Mary, had not seen Jesus in a post-resurrection appearance.
That is why Jesus sought to dispel his doubts by encouraging Thomas to touch him. Mary did not need such encouragement, however, since Jesus met her face to face. Her desire to hold on to Jesus prompted his cautionary words to her.
Second, as for when Jesus offered his blood upon the mercy seat in heaven, I suggest we exercise caution in taking that highly symbolic act too literally, which you seem to be doing, hence the second false premise.
After all, earlier in his earthly teaching ministry, when Jesus talked to his followers and others about the necessity for his disciples to eat his flesh and drink his blood, he was not speaking literally, but spiritually.
It is the Spirit who gives life; the flesh profits nothing; the words that I have spoken to you are spirit and are life (John 6:63 NASB).
What I am suggesting is that rather than attempting to attach a literal time frame to Jesus' offering of his blood at the mercy seat of God, perhaps a better tack would be to think of that offering as more symbolic than literal. After all, regarding the offering up of his blood to his Father, must we believe that Jesus took some of the literal blood he shed at Calvary and sprinkled it on the mercy seat? That belief does not, in my opinion, reflect a consistent and accurate hermeneutic, in light of the passage in John Chapter 6.