The CATH database classifies protein by fold: https://www.cathdb.info/
So the value from that is probably the most useful for you.
Reducing Agent Concentration
Your crystallising conditions do not mean much. They are a solution that is close to precipitating your protein but slowly enough for it ...
As a rough and ready and very easy to perform test I would put the entire universe of dsDNA through Primer3 (details below). This could be done by "splicing" your probe of interest onto each "chunk" of dsDNA you pass through primer3 and restrict the primer search to the 20bp primer you are interested in. In other words you are forcing the program to consider ...