What could "mucka doozy" mean and where does it come from?

I have heard a similar phrase in Scotland. Someone is "muckle dozy" if the are very stupid or slow-witted. This seems to fit the circumstances of your question, where light-hearted insult might be applied to someone who did not learn quickly enough.

muckle = >also mickle [mikl], arch. meikle [mikl]

adv. Qualifying a v.: much, to a great degree or extent, greatly

adv. etc. in the positive or comparative degree: much, greatly, very, exceedingly

Scots online dictionary

dozy = UK informal "thinking or reacting slowly"

Cambridge Dictionary

To add to my answer, I note that many immigrants to the east coast of America were from Scotland. They would have brought their language and vocabulary with them, including the word "muckle", which goes back to the 1700s or before as in the Dictionary of the Scots Language (DSL) below. It is therefore likely that the word would be used to qualify the linguistically more widespread "dozy".

I restrict myself to merely three of the many early DSL examples:

Muckle = Of quantity or degree: much, a great deal of, a lot of (Sc. 1808 Jam.).

“Contrair to just Rights and Laws I've suffer'd muckle Wrang.” Abd. 1768 A. ROSS Helenore (S.T.S.) 64:

“Yes, yes, twa men I saw, ayont yon brae,” She trembling said; “I wis them muckle wae. ”Edb. 1773 FERGUSSON Poems (S.T.S.) H. 193:

They are fear'd for denial o' quarter to themsells, having dune sae muckle mischief through the country.s.Sc. 1859 Bards of Border (Watson) 8:

[Scots Language Dictionary](Dictionary ](https://www.dsl.ac.uk/entry/snd/muckle)

You may like the recent use of muckle in:

"PM branded a ‘muckle glaikit numpty’ as SNP conference debates Scots language"

London Economic

(I Leave the definition of "glaikit" as "an exercise for the student")