You may run into some interesting shift aerobics. You could install a low C and if shifting is not manageable replace your A with a solo F# tuned to G (C,G,D,G). Also, I regularly go on my low C right up and above the mid harmonic, it is not difficult and the big string is very playable with the bow.
For playing classical I considered closely whether to get an extension, 5 string or tune in 5ths.
5ths work for me. I had no issues with the new fingering, even though I have about 45 years of playing in 4ths. The switch was no problem. I have compared my low C side by side to a fine old Italian with C extension with favourable results. Yes, the Italian was better but not by much. I recorded it on my phone and actually cannot hear the difference in the recording, only live. That’s why I joke my low C can loosen gold crowns.
I don’t buy what everybody says about the extra string length extension always blows away a regular length C. Depends on the bass. Five strings or a bass with a C extension both have way more top pressure than a 5ths bass.
I have installed many low B strings tuned to C. None have been difficult or poor to play. Obligato, Jargar, Spiro RM, Spiro regular. Spiro is my favourite for the low C. It’s a beautiful string.