Think of it this way - it’s “have had” because

“I had too much to eat” would be past tense, meaning you ate too much, say, last week

“I have too much to eat” is future tense, meaning you went to the buffet and got carried away, now you’ve got a massive plate of chicken in front of you

So "I have (right at this moment) had (just ingested) too much to eat (and now I’m farting a lot)

Also, in this case “to eat” isn’t a noun, it’s the infinitive verb