your best bet is to find a G4 quicksilver or MDD with a broken PSU. no more than 20-30 euro if you can fetch it yourself.
the chance is high that "broken" computers contain one of the standard graphic cards which these macs once shipped with.
but i have read your original question now and i would like to add here that you probably only have a problem with your specific monitor model or got something wrong with some settings.
because a GPU which works in a G4 would normally always support resolutions such as your 2k monitors. even the voodoo 3 from times years before the G3 processor give you 2000*1500 at the analog port (for normal 2D, not for games)
a geforce 2 MX lets you run 3D games in 1920*1200, a geforce 4 MX does the same for two monitors. analog and 2d is somewhat higher again.
if you dont find macs or cards at an acceptable price, it might be cheaper to get yourself other 2k monitors which will match better. but try multiresolutions and switchres first. they might offer you more settings than MacOS alone.
ADC adapters are unfortunately hard to find, i paid 15 euro for my last one and had to search about 8 weeks to find it.