The isogeny-based scheme CSIDH is considered to be the only efficient post-quantum non-interactive key exchange (NIKE) and poses small bandwidth requirements, thus appearing to be an attractive alternative for classical Diffie–Hellman schemes. A crucial CSIDH design point, still under debate, is its quantum security when using prime fields of 512 to 1024 bits. Most work has focused on prime fields of that size and the practicality of CSIDH with large parameters, 2000 to 9000 bits, has so far not been thoroughly assessed, even though analysis of quantum security suggests these parameter sizes. We fill this gap by providing two CSIDH instantiations: A deterministic and dummy-free instantiation based on SQALE, aiming at high security against physical attacks, and a speed-optimized constant-time instantiation that adapts CTIDH to larger parameter sizes. We provide implementations of both variants, including efficient field arithmetic for fields of such size, and high-level optimizations. Our deterministic and dummy-free version, dCSIDH, is almost twice as fast as SQALE, and, dropping determinism, CTIDH at these parameters is thrice as fast as dCSIDH. We investigate their use in real-world scenarios through benchmarks of TLS using our software. Although our instantiations of CSIDH have smaller communication requirements than post-quantum KEM and signature schemes, both implementations still result in too-large handshake latency (tens of seconds), which hinder further consideration of using CSIDH in practice for conservative parameter set instantiations.