Hi Steve
As they say "Welcome to my world" ive been going through exactly the same thing, no doubt you have found that builders & AV wiring dont seem to equate. I do have a heck of a lot of cable in my conversion, but I have to keep stressing to them that they must not bend kink or cut any of my cables I must p**s them off at times
They were desperate to board the floor & I still had the Cat5 & Speaker cables to run, it was a mad panic & took longer than expected, luckly they have been a bit slower in boarding the walls & ceiling so I have managed to get a HDMI Cable to the projector & Bed/TV
If I were you I would stick some large trunking in & a draw wire. I have used square drain pipe in the past this allows you to get scarts(not that any of us use them now do we

) mains plugs, vga cables & hdmi cables through with ease. At the end of the day the channel will be covered so it dosent matter what you use just make it big enough. I dont have an experiance with Cat5 & HDMI convertors but sounds expensive to me.
Cheers
Stu