Varnishing stairs that have been previously stained

[dutchcloggie]

Hi,

I have removed the ugly carpet from my stairs and I was planning on painting the risers white and the steps varnish. But after scraping the paint off the steps, using both NitroMors and a heat gun, the treads don't come out looking all that well. In the past, it looks like the middle section was stained an I cannot get the staining off the steps. I have sanded and sanded but it is no use.

So, question:
Can varnish cover underlying colour trouble with the steps and make them look a uniform colour (I know staining won't) or will I have to accept a Ye Olde Look? I most certainly do not want to paint the treads.

Thanks.