I'm pretty sure the "500 kbps" is a 25 year old typo in the manual. That has to be 500 kBytes/second, corresponding to the transmitted rate you're seeing. It doesn't make any sense in the "Master" section, as you have no control over the rate once you give a buffer to the SPI module. You can't slow it down unless you send one at a time, and why would you do that? It has to refer to the maximum "slave rate" the chip can handle, especially if using a higher clock rate (slave can use 12.5 MHz).
You'd be way better off finding a compatible PHY chip. You won't have to change any software in order to use it. Unless you need to handle some chip configuration.
But you've got about 25 years worth of technology to catch up on, which you don't need, can't use and don't want. But it will still cause you some problems.
The LXT905 only had one job to do (be a 10MHz PHY chip) and it did it well. Since 1995 we've had 100MBit and 1 GBit Ethernet, and so that why MII and RMII were invented. Some of these PHY chips are also multi-port Ethernet Switches which can connect 10 to 100 Ethernet themselves. There's probably more transistors inside some of these chips than in the whole MC68360!
If you can buy a very simple (1995 design) PHY that just does that then it should be easy. The TI DP83910A looks to be one of these if it is still available.
So any replacement chip you select is likely to have a lot of necessary options that have to be set somehow. It would be nice if you could do all this by mode pins, but they want to save pins as well. So you usually configure these chips through a weird serial interface, defined as part of the MII spec, and consisting of an "MDC" and "MDIO" pins. All Ethernet controllers built into chips provide and control these pins - all modern ones, but not the MC68360. It has two pins, like I2C, but it isn't I2C. It is like "Bidirectional SPI", but there's no Chip Select. You can probably bit-bang the pins if need be, or you might be able to program the SPI port if you have to.
The following is "generic experience" with other PHY chips. The chips you find that support this old and original interface may be easier or harder to use than the following. I'm just writing this in case you run into these problems I've had. If you can get the 28-pin DP83910A you won't have any problems. If you get the 48-pin DP83848 you'll have TWELVE strap pins to deal with.
Edit: Actually you would have a lot of problems with the DP83910A. It isn't a Twisted Pair adaptor, but the is made for the original Ethernet generation, where the interface was a 15-pin "D" connector called "AUI" requiring an external coaxial transceiver (10BASE2 "Thinwire" or 10BASE5 "Yellow Hose"). The DP83910A converts to AUI. You then need a separate DP83922 to get that to Twisted Pair. Also, if you look at the LXT905 you'll see it has two "Mode" pins. It connects to four DIFFERENT types of SNI interface. Yes, this "standard" had four incompatible variants, It could handle MC86380/AMD, Intel, Fujitsu/Seeq and TI. The LXT905 was brilliant because it could emulate the other four interfaces in the one chip. Anything emulating an Intel chip probably uses the Intel variant. The TI chips may only connect to TI chips. So which interface variant does the TI 83848 use? The only thing in the manual is the unhelpful "While there is no defined standard for this interface, it is based on early 10-Mb physical layer devices." I'd guess it is the TI variant and wouldn't work with your Motorola chip.
You're better off finding a way to use the chip without this serial port. So they usually have "strap pins" which you pull up or down during chip reset (to configure them), and these pins take on other functions after reset. So you usually put pullups or pulldowns on these pins to set the reset state. This is fine for pins that the chip uses to drive LEDs. It is also fine for signals going from the PHY to the Ethernet controller. Where it is problematic is when they use OUTPUT pins driven by the Ethernet controller to be pulled during reset. That requires the Ethernet controller to not drive these pins during its reset (or it will override the strapping). You can do that if those pins aren't dedicated (and can be GPIOs) on modern CPUs, but I don't know if this is the case on the MPC860. Hmmm. The only pins like this are TDX/TX and TENA/RTS.It looks like they're also GPIO pins, so you might be OK with this.
You should have last-time-bought a big box of LXT905s when you could. Google finds LXT905s for sale. You might be able to get enough to keep going.
Good luck.
Tom