Max, I don't think there's much you can do. The text boxes are converted to images. Depending on the resolution of your screen, these images will appear slightly blurry, since they now are no longer text, where characters are represented by fonts of different sizes, but rather a snapshot of pixels that may appear to run into each other.
You can try and hold down the Ctrl button while scrolling your mouse wheel in the browser window to zoom into the page and notice how the blur factor changes as the images are presented with differing resolutions, but essentially the blur is a result of the image being resized to the resolution Excel deems fit.

When saving as a web page choosing the option to save as "Web Page" gives you the pictures as *.png files in a sub folder, which you could then manipulate to save to a resolution of your size. Choosing the option "Single File Web Page" is less flexible, and, for example, will not open the page correctly in Firefox.

Maybe not the answer you're hoping for, but I'm still learning myself.

cheers