>One simple fix would be to make random order the default setting. Fixed in the sense that the bias will be random. Presumably students graded last will still receive lower grades.
From my experience as a tutor, yes, this bias exists. But it won't turn a horribly wrong or an excellently correct solution into anything else.
I eventually knew my strugglers and my excellers. I'd skim the excellers first, because if they messed up, something bad was going on. Then I'd go through the strugglers to see problems. And then I'd grade the rest first in whatever order I got the sheets, then the strugglers and then the excellers. I needed the baseline to see how bad the worst ones actually do. Some exercise sheets were an accidental adventure, I can tell you.
And writing it like that, it sounds totally callous and cold. But focusing on the lower third in the exercises and communicating their struggles to the TA and prof was very appreciated by everyone, especially those students. It makes sure to get the important fundamentals right.