hdmi to vga adaptor should do its job, as it was designed to transform one connection to the other.
this means the adaptor has video and audio digital to analog convertors.. and they are probably lower quality than the bluray player or cable box.
the hdmi to vga adaptor is a waste of money and a waste of fidelity.
digital to analog convertor chips quickly demand one adaptor being highly superior to another adaptor.
since the projector has a vga connector.. you might be able to 'overclock' the projector to get a higher quality result by using the 'powerstrip' software.
vga carrys the horizontal and vertical sync signal.. and if you refer to your projector specifications, you might find the scanning to be lower than what the projector...