Actually, the judges have a financial interest in declaring the income tax unconstitutional. They pay taxes on their salary; declaring the income tax unconstitutional would result in an increase of their takehome pay. They are immune from the downside because their compensation cannot be reduced under any circumstances, and they have lifetime appointments. Congress would just have to suck it up and pay them from some other means of raising revenue.
No salaried judge should sit on a tax case. They should recuse themselves and yield to a special master (maybe a retired state judge) without the personal financial interest in the success of the income tax.
In order to have someone in charge of the case who has no interest in the outcome of the case, you'd have to select someone whose tax burden is precisely ZERO--i.e., they pay no income taxes, and do not get the EITC.
Retired state judges do not meet this criterion.
IIRC, there is precedent for Congress closing entire courts and retiring the judges. Something from the Jefferson administration or thenabouts. I don't know if the precedent's been overturned or not.