Without seeing your HP "harness" it's hard to understand exactly what the difference is. It is quite acceptable to "leave the pins unprotected", they don't come under any stress. it sounds like the HP leads have a custom adaptor for their own m/board. It's unlikely, as you're finding, that it will match the pins on your new board. just make sure you get the correct leads on the correct pins. The pc won't finish the post without ram, so you won't know about the graphic card until it's all complete. Have you looked on the web for a .pdf manual for your new m/board? I know that pc chips aren't the best for web support as their site is sooo slow!
Their manual resides
here
i don't know if its any more comprehensive than your one page item.
Ive downloaded your manual which will give you more info than the sheet that came with your purchase. I suggest you do the same.