Well if you don't have a multimeter it would be tricky to do but if you have one you can check the voltage on a unused 4 pin(the ones that goes to the drives) connector, put the multimeter in voltage mode, make sure that the probes are inserted on the correct connector on multimeter(most of digital multimeters have the multi function socket and one dedicated to current measure, never insert it on current measure when measuring voltage!!!) and probe the yellow and black wires.

Speedfan is getting it's info from the motherboard sensors, so I would trust the BIOS value is probably the most correct interpretation of what the sensors say.
However, motherboard sensors are themselves unreliable. It's much, much better to use a multimeter as legacy described.

Nowadays I always use a meter to verify voltages on a PC build.
In addition, if I see disturbing voltages appear in a BIOS or Speedfan reading I also check that with a meter. I usually find that the real voltage is completely different from what the BIOS/Speedfan are reporting.

If you really are getting 11.7V on your 12V rail then I'd be unhappy with that. Yes it's technically within the +/-5% ATX spec but it implies a PSU that can't keep up or does a poor job of regulation. It can also contribute to instability.
However, if you put a multimeter on it, I'm guessing you'll find the real voltage is much closer to 12.0-12.1V, which is where a good PSU ought to be.

Often, when power issues are suspected, people are inclined to swap PSUs rather than take measurements. But I believe in taking measurements. If you work with computers or other electronics very often, a multimeter is a good tool to have, even if it's just for checking PSU voltages.

I have a multi-meter and will do so, I just wanted to ensure something wasn't very wrong with the board/PSU

While you have the multimeter out, also check the ripple (at load) to make sure it is within spec. If it is close to being outside of spec, recap the power supply before you release the magic smoke.