Blu-ray on older "HD-ready" Mitsubishi TV?

[lumpster]

Perhaps a naive question, but I have a 6-year old large screen Mitsubishi that claims to be "HD-ready," but no HDMI inputs. A careful reading of the back of the Mitsubishi manual seems to indicate that the TV will accept (and display) 1080i via the HD component inputs. So, several questions:
1. What's the right way to get closer to Blu-ray quality out of a Blu-ray disk
on this TV? A little bit of research seems to say that most Blu-ray players
will only display 1080p out of the HDMI outputs, but not the component
outputs. Am I reading the Blu-ray documentation correctly?
2. I've seen several HDMI-to-component converter boxes, but will I run into
1080p-to-1080i conversion problems?
3. Am I trying to do this the hard way, and I should just go buy a newer
1080p HDTV?

Some help that would keep me from making an expensive mistake would be most appreciated...