Some video drivers can correct for overscan, meaning they output the video mode normally but downscale the content to the middle 95% portion of the video for example.
VGA to RCA RGBHV breakout cables are very, very rare but there is at least one OEM still making them. I found a 1.8m one for sale online for US$24.
From searching dtvforum.info I found these 720p settings:
Scan Rate: 38.164Mhz
Active Pixels: 1280 Pixels
Front Porch: 451 Pixels
Sync Width: 40 Pixels
Back Porch: 357 Pixels
Total: 2128 Pixels
Scan Rate: 50.018Hz
Active Pixels: 720 Pixels
Front Porch: 5 Pixels
Sync Width: 5 Pixels
Back Porch: 33 Pixels
Total: 763 Pixels
+ve pol +ve pol
I've got an HR36 which is,or at least should, be identical to the HX32 except in size and grille pitch. Its overscan isn't as severe as you've experienced but I'll be looking to correct it.
The service manual can be found here
The service menu is probably identical to the HXs'. You do need to be careful in there as a large mistake can brick the TV. There is an error in the service manual where it says to press Mute + Jump to save - it should say Mute + 0.
I have found, and I presume the HX is the same, that there is a severe red push on 720p60 and 1080i60 by default. I corrected this by going to the COLOR section and changing the AXIS setting from 3 to 1. Or you could edit the items in Color->Standards *3 AXIS3 to be the same as AXIS1 to make it global to all video modes with AXIS3.