I don't know what the options are for the DOJ.  Will the DOJ just appoint another US Attorney to the cases, or will the DOJ take the case to the Appeals Court and, if necessary, to the Supreme Court?

Note that the judge does not claim Comey and James are innocent or that the evidence against them doesn't exist or is not valid.  The judge merely asserted her opinion that the US Attorney was not properly appointed.  The Democrat Judge's claim has nothing whatsoever to do with the legitimacy of the charges against Comey and James.

Clearly, the Democrats' plan is to delay prosecution of the criminals, hoping Trump's term will be over before the situation is resolved in the slow moving courts.

There is no doubt whatsoever about the guilt of Comey and James.  The doubt is whether any Democrat can be held accountable to law.  There simply may not be any prosecutors in the DOJ that will prosecute the cases.  Even though it is a "Trump administration," the federal bureaucracy is composed almost entirely of partisan Democrats dedicated to the Reconstruction of America.