"more neatly" is correct and usable in written English.
You can use it to describe the way something is done or presented, for example: "He arranged the items more neatly on the shelves."
The Brooklyn show is the smaller and more neatly packaged.
Turks divide more neatly on the matter of Pamuk himself.
The first inning could not have stuck more neatly to script.
In Ms. Hegarty's first solo at Nicelle Beauchene, the damage is more neatly contained.
Snyder's Hitler is no doubt made more neatly uniform in purpose than he really was.
For a start Braine writes much more neatly and truly than anyone else.
Often they tend to treat vocals as one more neatly placed sound effect.
His pitch for the job could not be clearer or more neatly aligned with government thinking.
No horticultural buzzword sums up the current mood of UK gardening more neatly than "heritage".
They want decoration, order... more neatly trimmed shrubs, fewer cabbages, marrows and stringy beans.
I'd like to write more neatly, even though people don't send many handwritten letters these days.
