There are just a few DVD units that will upconvert over component. Like you I have a 2002 model Mits RPCRT HD TV that has only component inputs so I went through the same search. There are some good threads on this over at the AVS Forum site too. What I found are models from Zenith, Oppo, Samsung and maybe one more, I think it was Momu (SP?) . I believe all of these have an MSRP below $300. I think most of these units, if not all of them, also have DVI or HDMI outputs for a future TV purchase should that be a consideration. Each brand had different methods to make it upconvert over component. You should research those forum threads and look for brand availability in your area to help you make a choice. This whole thing is a gray area though as the manufacturers don't advertise or acknowledge this upconversion via component as a feature because it bypasses the whole HDCP protocol that they are supposed to be supporting.
I purchased a Samsung HD950 because it did not have the Faroujda chipset that can display the macroblock bug on some TV's. It is also black which matches my other components and plays SACD and DVDA discs. To make the Samsung's upconvert over component you have to push a series of buttons on the remote which makes it HDCP free allowing the upconversion. I am pleased with the result. It looks very good on my TV, not quite HD compared to OTA HD broadcasts but as close as I have ever seen any DVD displayed on my set. There may be units out there that display a better picture via 480p than I am getting now, but those units would be significantly more $ than what I was willing to spend.
Just one hint. Make sure to use an input on your TV that will accept the higher rez signal. Although my TV (Mits WS-55511) has multiple component inputs only one of them will accept anything above 480i/480p. I found this out after about a week of futzing with the Samsung every night and not understanding why it would not display anything above 480p even though the remote "hack" appeared to work. When I finally got down behind the TV with a flashlight I could see the labels on the inputs. As soon as I switched to the lone input labeled for 480p-1080i it worked great.