maybe you could try the little converter plug you mention but otherwise, if you start trying powered video converter boxes to get the signal from your pc to something your monitor can display, you might run into problems as a lot of those boxes are just cheap unbranded chinese stuff, so you might get display lag, sync problems, poor picture, interference, limited resolutions, etc.
im surprised that monitor you have doesnt have more/better connections, especially considering it is a sony. you could buy an expensive converter box, but for the money you could get some different pc hardware instead etc. i used to like composite, but once u go to rgb its hard to go back to it. as for svideo, i dont know how that would look, i havnt tried that. im not sure but with svideo you might be stuck on one screen mode only, eg. 640x480. same with composite i think. im guessing you dont mind that though as you have used composite before in the past