Sorry yes my point was to make the Pi an offload processor from the QL (which could provide many more functions and be very standard / cheap for people, so I drifted off topic about how to do that; the idea of putting it on the memory map will allow fairly rapid write even with the limit of the Cartridge port being Read only using address lines for write - I was hoping to direct connect to PI GPIO somehow perhaps with a standard buffer chip).
The Max232 should be able to do 115kbs but as you say TCP/IP would need faster, hence my suggestion of ignoring the serial issue and using the PI TCP/IP stack - the PI also has TTL serial so over a very short distance it should be able to be ramped up really high. Once you can get at it, it also has an SPI interface anyway that can use the WizzNet but again a PI0W has Wifi if that was OK - depending on size constraints using a bigger Pi will give an integrated CAT5 connection.
I was looking at perhaps the memory mapping technique
http://theqlforum.com/viewtopic.php?t=389 discussed in this post to communicate with the PI - the post with the technique talks about a direct SPI drive he designed connected to teh Cartridge port - so maybe that it is the way to talk to the PI for me and or your Offload WizzNet directly - we both get what we want...
...and the QL scene gets a new BUS standard we can use for modern products. (hinted at in the same article but, not explained).