[Grammar] to propose to include

Is this sentence correct?
- I am writing to propose to include the other three measures in the handbook.

I find the '''to propose to include' a little weird.

If that sentence is correct, then can I write like this:
- I am writing to propose including the other three......

I like the sound better. Any difference between the two?

Thank you.

I [am writing to] propose that we include ...
I [am writing to] propose including ...

In the context of a letter that I am writing to someone, so I started with, "I am writing to...."

In this case, is "I am writing to propose including the other three......" correct?

Thank you.

What you quoted looks okay, but we'd need to see the full sentence to confirm that.

For example, say I write an email to the librarian to include some books titles in the reading programme list.

- I am writing to propose including the other three titles in this year's reading list. The reason is.....

OR should I write: I am writing to propose to include the other three titles in this year's reading list. The reason is....

Thank you.

Exactly as emsr2d2 said in post #2.
Either "including" or "that we include"

I'm not a fan of "I am writing to..." as an opening.

Regarding this year's reading list, I would like to suggest that we also include...