The other Henry J. Johnson's were from different parts of the State. The one who served in Co. C, 1st Arkansas Infantry, was from Ouachita County; the one who served in Co. B, 17th Arkansas Infantry, was from Sebastian County; and the one who served in the Desha County Militia was from Desha County.
I wouldn't bother requesting the CSR for his service in the 30-day volunteers, unless you just want a copy for your records. The record consists of only one abstract card, which I transcribed and posted on the Gerdes page. You should definitely get a copy of his record in Newton's regiment, though. It contains some additional POW information not posted on the Gerdes page.
You can get a copy by clicking on the big white banner at the top of this page. It's much faster than going through the Arkansas History Commission.
NARA filed the records for Newton's cavalry as the 8th Arkansas Cavalry. The roll you want is Roll 28. For the 1st Arkansas Volunteers (30-days) it is Roll 44.