Steve,
Your information on the Tate house is about as best as I could do, so I cannot help you there. As for the Lowe house:
--Connelley's 1910 book on pages 251-2, wrote this action took place in the Jordan Lowe house, about 12 miles SW of Independence, which would place it roughly in the Little Santa Fe area, too.
--William H. Gregg's manuscript on page 1-2, said the vacant Lowe house or cabin was 16 miles SE of Kansas City, which--based on Kansas City's size and location at that time--would place it along an arc from about Stony Point in east-central Jackson County to as far as about Hickman Mills in southwest Jackson County, if we are talking about "as the crow flies," and not road miles--which would be shorter in straight-line distance.
--The "Kansas City Daily Journal of Commerce" of April 17 and 24 wrote the small, old Lowe house was in the direction of Little Santa Fe, two miles from any traveled road, and about 12 miles from Independence, and that the Federals of the 1st Missouri Cavalry burned the place after the fight.

Applying the 1860 census to this problem, of the five Lowe households in Jackson County at this time, the A. W. and Calvin V. Lowe households were in Sni-A-Bar Township of NE Jackson County, and far from the two location discriptions given above, and so was the Schuyler Lowe household of Independence Township. This leaves the John R. and John M. Lowe households of Blue Township as being in the area of the two locations cited above. Connelley wrote the log cabin was associated with a Jordan Lowe, not named in the 1860 census, at least as a head of household, so if you find Jordan Lowe in the 1850 census, you might estimate from the names of his neighbors a more precise location.

That's about as close as I can get.
Bruce Nichols