Maybe this is a heretical question, but why is either of those spellings not just a mistake?
Shouldn't it just be two words,
In every other analogous case, 'full' is a word, not an unaccented suffix, and the adverb answering the question 'How full?' is a separate word or phrase.
full to bursting
full to the brim
The suffix -ful, in contrast, never has the main accent, because it has a different meaning and a different grammatical function.
a handful of coins (How many coins?)
a capful of lemon juice (How much lemon juice?)
a basketful of flowers (How many flowers?)
Her bridge hand was full of kings and queens.
He filled his cap full of seashells.
A cornucopia is a basket full of the bounty of the harvest.
His hat brim was full of souvenir badges and pins.)