I found r8169100.zip which is David's BETA release of the chipset driver
The beta driver has some very serious problems, depending on which Realtek chip you actually have (RTL8111DL doesn't tell you that). The proper driver works well, and you can get it (with support) from Arca Noae:
https://www.arcanoae.com/about/If you don't want to pay for Multimac, you should try the GENMAC driver. Again, depending on the exact chip, it may, or may not, work (and there is no support). There is another, older, driver rtgnda13.zip which will probably work, but I don't think it works with NETBIOS (I think it was okay with NETBIOS over TCPIP).
The main problem that I see, with Realtek NICs, is that they are SLOW (even in windows, they are much slower than Intel NICs). This seems to be a known drawback with them, on all platforms, but it seems that they are cheap, so manufacturers keep on using them. FWIW, I would not be surprised if your 100 mbs 3c905B would be just as fast as a 1000 mbs Realtek device.
You may also find that NETBIOS will not work with a lot of other things, like routers, and WiFi devices, that don't know about it. NETBIOS over TCPIP usually works with them.
NETBIOS also has a number of limitations that make it unusable with other operating systems. The fix for that is to abandon NETBIOS and use SAMBA (which is effectively the same as NETBIOS over TCPIP, with support for large files, and modern security).