There is much I have to say to you

I think the second, if I understand what you're driving at. the "to" at the slash definitely goes with the "say," not with the "have."

I need to say this. The infinitive "to say" is direct object of the verb "to need."

I'm not sure where you're coming from with "have to." Sometimes little kids use it. "Aww, do I have to?" "Go to bed!" (reply) "I don't have to."

<I need to say this. The infinitive "to say" is direct object of the verb "to need.">

Isn't that "need to", an auxiliary?

<I'm not sure where you're coming from with "have to."><

?? Have to" is a, relatively, ages-old semi-modal auxiliary. It's used by children and adults alike.

Okay, now I'm with you.

IMHO the answer is "No." In your original example, it's "have / to say." Likewise, "need / to say."

There may be exceptions, but I think your example is more like "I have this to say." "Have" indicates possession. "I have two three tickets to the game."

I have this to say = I have to say this

Hi,
There is much I have to say to you.

Would that be read as:

There is much/I have to/say to you.

or as:

There is much I have/to say to you.''

I'd take this to mean "It is necessary for me to say a lot to you'.

For the other meaning, I'd instead say 'I have a lot to say to you' or I have a lot that I want to say to