I found some records for early Atwoods of Maryland--just clues. I couldn't find proof to connect James to anyone earlier, though there was a will for a Charles who had a son James. See below.

Henry C. PEDEN's MD Deponents: John ATWOOD, Anne Arundel County, aged 66 in 1706.

Abstracts of Land Records of Anne Arundel County:

Philethia/Phylothia STANDFORTH, dau/o Jno. of Herring Creek, received a cow marked with a crop in the left ear and a swallow fork with slit in right ear, gift of Jno. WHIPPS, Sr., her grandfather. She has another cow, named Promise, with same marks, gift of Jno. ATTWOOD of Herring Creek, recorded 10 Nov. 1701 & 10 Nov. 1707.

Richard GOTT, AA, with dower released by Eliza. GOTT, deeded, 16 Feb. 1709, to Henry ATTWOOD, AA, carpenter, for forty-one pounds sterling, "Carpenter Yard," 52 acres, part of "Ram Goat Swamp" by a marsh by the side of Gott's Creek.

F. Edward WRIGHT's Anne Arundel County Church Records of the Seventeenth & Eighteenth Centuries, St. James:

Wm. Horn, b. 15 8ber 1710, bu. 17 7ber 171_, s/o Jno. ATWELL & Margt.
Jno., b. 29 7ber 1712, bu. Je. 1713, s/o Jno. ATWELL & Margritt.
Jno. ATWOOD bu. 1713 {exact date not given}.
John ATWELL bu. 10 Aug. 1719.
Henry ATWOOD m. Jane PRATT, 9 Feb. 1718/9
Elizabeth ATWOOD bu. 5 Dec. 1720
Jane PRATT bu. 13 Dec. 1720
Jane ATTWOOD, b. 19 Mar. 1720, d/o Henry & Anne
Peter, b. 2 Feb. 1726/7, s/o Henry ATWOOD & Ann
Jane ATWOOD m. 27 Dec. 1733, Francis CRANDALL.
[I don't know whether ATWELL was the same family as ATWOOD.]

Robert BARNES' MD Marriages verifies the marriage, 19 Jan. 1768, at St. Inigo's Catholic Church, St. Mary's County, of James ATWOOD & Henrietta JARBOE. The only other ATWOOD in Volume One of MD M. is Henry ATWOOD, m. 9 Feb. 1718/9, Jane PRATT, at St. James, Anne Arundel Co.

Volume Two, 1778 - 1800, doesn't have any male named ATWOOD (but not all marriages are included).

Volume Three, 1800 -1820: John ATTWOOD m. 13 Mar. 1808, First M. E. Church, Baltimore Co., Cathe. KIRKLAND.

MD Calendar of Wills:

John ATTWOOD, planter, St. James, AA, 15 Nov. 1713, 20 May 1714. To wf. Eliza & son Henry. Wit. Eliza FARMER, Jas. MARR, Chr. VERNON.

Henry ATTWOOD, AA, 20 Feb. 1729, 31 Mar. 1729. To dau. Jane, dwelling plantation in Baltimore Co. and 100 acres bought of Jonathan TIPTON. To wf.__. Wit. Wm. FORD, Joseph PRATT, Robt. KENDALL.

Charles ATWOOD, St. Mary's Co., 22 Sep. 1773, 16 Apr. 1774. To wf. Trasa / Tereza / Teresa, exx., and to ch. Ann, Charles, Elizabeth, George, & James. Wit. Wm. TAYLOR, Sr. & Jr.

Abstracts of Wills of Montgomery Co., MD, 1776 - 1825, by MALLOY, SWEEN, & MANUEL:
James ATWOOD, 5 Dec. 1799, 16 Jan. 1800.
Wife Mary (coexx.); daus. Mary ELLIOT, Elizabeth GREEN, Ann MEDLEY, Cela, & Ellioner.
Sons James, John L. (coex.), Willy, George Perry, & Charles. Unborn child.
Wit. Joseph JARBOE, Henry BELWOOD, Josiah BEEDING.

{Notice that his wife was Mary.}

Margaret MYERS' Marriage Lic., Fredk. Co., MD, 1778 - 1810: Elizabeth ATWOOD, 29 Sep. 1796, William GREEN.

Marriage Licenses of Montgomery Co., MD, 1798 - 1898, by Janet T. MANUEL: ATWOOD,
George P., 5 Nov. 1813, Anne CLEMENTS
Ann E., 7 Jan. 1833, Benjamin THOMPSON
Annie L., 25 Sep. 1889, Henry C. JAMES
James T., 18 Dec. 1890, Pearlie J. HOWSER.

Fredk. Co., MD, Militia in the War of 1812: William ATWOOD m1. Sep. 1817, Fredk., MD, (date was per the widow, though license was dated 19 Feb. 1818) by Catholic Priest MARONEY, Priscilla HILLEARY, b. ca. 1795. Wm. d. 22 Sep. 1852, Loudoun Co., VA; widow res. Newburg, Preston Co., WV, 1866 - 1878. Widow said he served under Capt. Denton DARBY. He was drafted 10 Je. 1814 for six months at age 23, carpenter, born near Poolesville, Montg. Co., MD; six ft. tall, dark eyes and hair, fair complexion. He lived in Montgomery Co., MD, till 1816; Fredk. Co., MD, till 1847; then Loudoun Co., VA. Witnesses in 1878: F. M. FORD, 45, & C. W. FAWCETT, 34, both of Kingwood, Preston Co., WV. Source = Pension WO24349, rejected, record not found.

Can you think of any other clues?