Daniel, I did a census check of all the Packard's in OH in 1830 and here is the list:
Alanson Packardno females age 5-under 10 b. 1821-25 but he does have 1 female under 5
Henry Packard 1 female 5-under 10 b. 1821-25; 2 females under 5 Henry Plackard w/alt Packard2 females 5-under 10; 1 female under 5 Jacob Shackard w/alt Packard no females younger than 15
CUYAHOGA CO Isaac Packard 1 female 5-under 10 b. 1821-25
MARION CO JB Packard1 female 5-under 10, 1 female under 5 Phineas Packard no females under 15
PORTAGE CO Nathl Packard1 female 5-under 10 Zachariah Packard (sheet not readable)
GEAUGA CO Noah Packard1 female under 5 Thomas Packard(sheet not readable)
TRUMBULL CO Thomas Packardno females under 40 Thomas Packard (JR?) no female under 15 William Packard 2 females 5-under 10
In checking the 1840 Adams Co, IL census I found no Packard's however, I did find one in Hancock Co, IL which borders Adams Co.By 1840, Matilda Jane would have been about 15-16 yrs old IF 1824 is her correct birth year. Noah Packard has one daughter age 10-under 15 b. 1826-1830 in his household.He may be the same Noah Packard that was in Geauga Co, OH and appears to be your most likely prospect.
The only other Packards that I found in IL in 1840 were Robert Packard in DuPage Co (1 female 20-under 30) & Philip Packard in Pike Co IL who had no young females in his home, however, Pike Co is also a border county to Adams Co.
Since Adams Co is bordered by two MO counties (Marion & Lewis Co's) I checked MO and only found some in Van Buren Co (no longer exists) which was across the state & was on the western border of MO