I am also descended from Burwell Burchett and I will share what I know and try to explain the connection you seek.I am also curious as to where you found the genealogy relating to Judy Garland.If you need additional information, please contact me at firstname.lastname@example.org
I show that this Edward Burchett was the son of Edward Burchett Jr. and Mary (Ann) Drury both born in Chatham Kent England.Edward Burchett Sr. was born in 1640 also in Chatham Kent England.Siblings included Nicholas, Thomas, Daniel and Mary.Their father was Thomas Burchett born 1561 in England.His grandfather was Thomas Burchett born 1535 in England.
The Edward Burchett that you mention in the genealogy of Judy Garland was the son of Edward and Mary Drury as mentioned above.Other siblings were Thomas, Elizabeth and Robert.Robert, born about 1675, married Mary Platt in Virginia.Their children were Thomas (1720), Benjamin (1725) and Joseph (1730).Thomas married Elizabeth Ann Sikes in Virginia.Their children were Burwell (1748), William (1754) and John (1761).Now this Burwell also had a son Burwell Burchett II and a nephew Burwell Burchett by his Brother John.I am not sure which Burwell you are descended from, but if you are descended by any then you are descended from the Edward Burchett(s) mentioned above.
From Burwell Burchett Sr. I am descended from his son John tograndson John to Elbert Franklin Burchett, to William Ellis Burchett to Norma Joyce Burchett (married Billy Ray White).I hope this is helpful.Les White