Indeed, you want "much too" here. As was said in the ELU question @AhmbroDude linked to:
Too much modifies a noun and a verb, and much too modifies an adjective or adverb. (source)
To elaborate on this a little, notice that you can't put much directly before an adjective or adverb, except in the comparative form:
✗ That dog is much scary.
✓ That dog is much scarier than this one.
✗ He arrived much late.
✓ She arrived much later than he did.
✗ The film adaptation was made much quickly.
✓ The film adaptation was made much more quickly than the graphic novel adaptation.
This alone should tell us that "too much late" doesn't work.1
On the other hand, you can say too before an adjective or adverb:
✓ That dog is too scary.
✓ He arrived too late.
✓ The film adaptation was made too quickly.
Finally, much can come before too. If it does, not only does it mean "more than acceptable", but "a lot more than acceptable".
✓ That dog is much too scary.
✓ He arrived much too late.
✓ The film adaptation was made much too quickly.
1 Although the comparative does:
The remake was made later than the original.
The remake was made too much later than the original for the cultural references to make sense.