I had a serious problem getting good framerates from Rogue Squadron 3D as soon as I would install DirectX because the game seems to force Direct3D on you even when you want Glide, the latter of which has considerably smoother framerates on the Voodoo 3 than Direct3D.
In regards to Shadows of the Empire, I don't know if you can underclock the K6-III like you can with the K6-III+ (I personally use the latter), but this game runs too fast if its framerate exceeds 30FPS. I don't exactly remember how the game ran on the K6-III+ at full speed (450MHz on a 100MHz FSB, in this case), but I believe it ran too fast.
Ideally, the game should be run on overpowered hardware with a framerate limiter to keep the game steady at 30FPS, although I have yet to find any framerate limiters for Windows 9x. Those that are available work wonders for Windows XP to Windows 10, but I can't find any such tools for Windows 9x.
Creator of The Many Sounds of:, a collection of various DOS games played using different sound cards.