I thought that they sounded like Chicago. Jim Peterik is credited as the writer for Vehicle. He eventually moved on and helped form Survivor. Jim is credited for several of the hits for Survivor and 38 Special also performed some of his songs. For now, I won't spend too much time on Survivor and 38 Special, but will go ahead and link to the story for one of his hits. He is probably referring to La Grange, Illinois rather than La Grange, Texas. In their live performances, he is usually on keyboards.
I had you slotted with a heavy lean towards Zappa, Dylan etc. Your recent mentions of Canned Heat, Humble Pie, Small Faces, Psychedelic etc is causing me to rethink things. Humble Pie, Marriott, Small Faces? My pleasure. . More of a compilation rather than a live performance.