Learn English – Meaning of “very time”

You have to look up up to:

the responsibility or choice of (someone): 'It was up to them to gauge the problem', 'No one is forcing them to make a difference here, it is really up to individual choice'

And it could mean decided by someone.

"If the choice of topic were up to me" could be rephrased to:

'if I had the responsibility to choose a topic', 'if I were responsible for choosing a topic' or 'if I were (was) the one to decide what (which) topic to choose'

[Oxford Online Dictionary, The Free Dictionary]

You're mixing two different changes - one is including/omitting such. The other is switching between of and to. So there'll be four different cases. First, let's see about the of part.

1. The pain is of a degree that calls for morphine.
2. The pain is of such a degree that it calls for morphine.

In the first sentence, it's the degree that's being described. It's the degree that calls for (allows, rationalizes etc.) the usage of heavy drugs. One might say ...of a huge degree or ...of a degree that's huge.

In the second sentence it's the pain itself that is so intense that it requires a morphine injection. Both cases mean the same thing in practice but grammatically speaking, you need to watch what's being described.

And in the following examples, one can see that the first sentence makes sense. The second one doesn't feel right at all.

1. I was happy to such a degree that I cried.
2. I was happy to a degree that I cried.

What you could say is the following. This uses to a degree as a moderator. So you can substitute it for e.g. somewhat.

I was happy to a degree. I was happy somewhat.

One could also say this:

I was happy to a degree, so I cried.

meaning

I cried because I was so happy to a degree.

but that's not what you're looking for, probably.