The SPI clock settings is Ethernetx library dependent, you can change in the library or modify it to permit setting it inside your sketch.
For example, for modified Ethernet library w5100.h#L61-L77
#if !USE_W5100
// Safe for W5200 and W5500, but also tested OK on W5100
// Use 14MHz if you know your W5100 can't run
// Higher SPI clock results in faster transfer to hosts on a LAN
// or with very low packet latency. With ordinary internet latency,
// the TCP window size & packet loss determine your overall speed.
#warning Use 25MHz clock for W5200/W5500. Not for W5100
#define SPI_ETHERNET_SETTINGS SPISettings(25000000, MSBFIRST, SPI_MODE0)
#else
// Safe for all chips but too slow
#define SPI_ETHERNET_SETTINGS SPISettings(14000000, MSBFIRST, SPI_MODE0)
#warning Use 14MHz clock for W5100/W5200/W5500. Slow.
#endif
where SPISettings is defined in HardwareSPI.h#L37-L100
class SPISettings {
public:
SPISettings(uint32_t clock, BitOrder bitOrder, SPIMode dataMode) {
if (__builtin_constant_p(clock)) {
init_AlwaysInline(clock, bitOrder, dataMode);
} else {
init_MightInline(clock, bitOrder, dataMode);
}
}
SPISettings(uint32_t clock, BitOrder bitOrder, int dataMode) {
if (__builtin_constant_p(clock)) {
init_AlwaysInline(clock, bitOrder, (SPIMode)dataMode);
} else {
init_MightInline(clock, bitOrder, (SPIMode)dataMode);
}
}
// Default speed set to 4MHz, SPI mode set to MODE 0 and Bit order set to MSB first.
SPISettings() { init_AlwaysInline(4000000, MSBFIRST, SPI_MODE0); }
...
friend class HardwareSPI;
};
It's always better before designing a completely new hardware, do some basic research on the current implementation to have knowledge, make / test on some prototype and avoid costly mistake.
Anyway I guess it's so far so good for you now