Forstner style bits are easy to sharpen (and they need sharpening fairly regularly too, in fact they're often not very sharp even when brand new). That, along with selecting the correct speed, will fix burning.
This is what woodworking is all about, it's always easier and quicker to pause and get the preparation and tool maintenance right rather than try and patch up the job afterwards. Scorch marks run deep, and in two of the four quadrants you'll be sanding into end grain, so instead of a round hole of a specific diameter you'll end up with an oval of a different diameter. That'll likely cause more problems further down the line. Start again, do it right, and chalk it down to experience.
