You will be pleased to note that your Chronicles of Oklahoma reference was cited as the source of Figure 4 in my first reference on Phillips Expedition leading to the Battle of Middle Boggy. It says:
" Figure 4. Old Beale Wagon Road. Source: Grant Foreman, Chronicles of Oklahoma, Vol. 12, No. 1, p. 74. "

My main reason for finding Beal's Bridge location was to give added credence to the line of march for Phillips Expedition of February 1864, both in coming and going across the South Canadian near Old Fort Holmes. As Phillips was in a "burning mood" on his return march to Fort Gibson, it is possible that he burned the wooden bridge flooring and perhaps also may have damaged the steel framing. Following this line on his return, he march northward toward Wetumka, instead of eastward along the Beale Road toward Hillabee. I also think Phillips burned the Oak Ridge Mission School, located about three miles north of the Beal Bridge, as he past by on Feb 17, 1864.

I had not noticed that Beale's survey past by Mr. Airds' Place, which still existed in 1895, according to US BLM records.

Thanks for you comments and interest.