I did get thrown awhile back. He wants to play "Ramblin' Man" by the Allman Brothers. Not in G# like the recording, but in E. Some mental gymnastics to get there especially if you want to stay low.
This happens to most of us when we find we need the open strings. But I find practice make perfect (or at least good enough) here, as well. If you know your problem areas, you can practice those exceptions to the rules so that you won't be flustered when you need to incorporate open strings.
I play with a blues guitarist who uses a lot of those keys for his vocal range, and it's been helpful to me to practice his songs in his preferred keys, but not just for those songs - if he changes his mind and calls any song in one of those keys, I know where to go with it.
This is one reason I shy away from the often-heard advice to avoid open strings. There's no real reason for it, beyond the minor tonal differences associated with open versus fretted. But if you never play them, you will never have the magic under your fingers to play them when you really need to. And you won't have the flexibility to choose them when you really want to.
I play a song with a different band that does a 1-4-5 thing in the key of A. The progression starting on the A is A-E-G-G# and back to the A, repeat until the change. The E is an open string, so it goes low for that second note and walks back up. The change starts the same progression at the fifth fret of the A string, so it's D-A-C-C# with the A going low.
The beautiful thing here is that I have a choice. I can keep things consistent and also play that A on the open string, or I can choose to play that A at the fifth fret of the E string. Sometimes I choose one way, sometimes the other way. I have to sing through it, and they're equally easy for me. But it's nice to have the option of consistency on those first two chords, even though I will play the fully fretted pattern when I go up for the five.
The point is that little things like this, if you practice them and value them enough, will improve your choices if you think of them as opportunities to become more flexible rather than rules you have to break. I know that not everyone sees them as rules, but the thing about never playing open strings seems to be a rule for lots of folks.