I haven't got round to looking into installing my LAN module yet but I would expect it to use much more than 25 mA and from what you have found out it looks like the A1208 doesn't provide enough power on the 3.3v pin hence your LAN module not working.
The good news is that if you type in "3.3v power supply" on ebay, you will find loads of modules to convert higher voltage down to 3.3v.
Take a look at this one, its cheap and has the details further down the listing. There are only three pins ie IN 5 to 10v max, OUT 3.3v and GND.
https://www.ebay.co.uk/itm/DC-5V-To-....c100005.m1851
Pretty good and would also be handy for using 3.3v microdrives in the Amiga
He he, we are all learning something new as we go along