Imediately upon landing half the company bolted taking with them about 300 people, hundreds of horses, cattle and pigs. They just disappear from history, but so did everybody who went inland in North America. We are only now learning what happened.
The later De Soto expedition 1539/41 reached the Ohio Country and the Midwest. They visited places, did things, and may have set up some permanent camps for use by later visitors.
By that time the Spanish had already figured that North America was short on horses, cows, chickens and pigs ~ so they made sure every ship that came this way brought a bunch ~ which were promptly turned loose to forage.
They would be caught or hunted later!
Pizarro, a probable Spanish Protestant (certainly Carvajal was), worked for DeSoto. These fellows kept their Protestant proclivities to themselves but it's pretty obvious they wanted little to do with Catholic Spain once they got here.
Another item high on the Spanish list was GOLD.
They dug gold mines everywhere. A typical gold camp would have some houses, barns, a still (for alcohol to buy produce from the Indians), a grist mill (to grind Indian corn as well as gold ore bearing rocks).
We have two probable Spanish sites in Fairfax County along the Fall Line (where you can find gold). If any of you amateur archaeologists run across stone segments for a wheel in a grist mill out there in the dirt with no obvious explanation, bring in the professionals at the state university. Give 'em a chance to do some radio carbon dating. The site may be of historic interest and far older than you imagined.
Many of these places have been found located all over North America ~ most of them East of the Mississippi were abandoned before 1600. There was some gold ~ mostly glacial in origin, and easily worked out.
These guys moved on wealthy or not ~ in the 1600s the Iroquois managed to clear out all the Indians and Spaniards from South of the Ohio although they were unable to dislodge the tribes to the North. That may have been quite enough to convince the Spanish to simply abandon whatever it was they'd been doing there.
Of note, the first European cattle in Illinois, NORTH OF THE RIVERS, had long horns. The earliest European pig had long legbones and was clearly of the same breed commonly found in Spain.
Those animals probably didn't just walk across the Ohio or the Mississippi!
You wrote:
“Pizarro, a probable Spanish Protestant (certainly Carvajal was), worked for DeSoto.”
Pizarro was a life long Catholic. He never did anything that would indicate that he was a Protestant. He was baptized Catholic, worshipped ONLY in Catholic churches - might never have even seen a Protestant one - and helped build a number of Catholic churches himself. For crying out loud he laid the first stone of the CATHOLIC CATHEDRAL in Lima!!! Where do you get these bizarre ahistorical ideas of yours? Next you’ll be claiming there were Vikings in Russia in 1700! Oh, wait...you already did.