Based on the styles shown above, it could also be argued that your Ducal Patent is an Honour or Ceremonial (i.e. Administrative/Bureaucracy) Patent rather than a Landed (proper) Representative Patent like the Baronial Patent.
In other words, the Baronial Patent is styled "Baron of Khalu", which is the unique styling for the Landed Representative of the World before the Moot and the rest of the Subsector/Sector (as opposed to, for example "Baron of the Third Imperium", with Khalu simply listed as the world association underneath, which would be an Honour or Ceremonial title with fief-lands on Khalu).
"Duke Gary Seebo" could simply be an Honour or Ceremonial title granted to the Baron, with the Dukedom styled in the last name of the Patent Holder, with fief-lands on (rocks in ?) Glisten and other worlds about the Spinward Marches Sector per the Ducal Land Grant parameters. Perhaps the Landed Baron was promoted to a Senior-level administrative posting within the Imperial Bureaucracy of the Spinward Marches or the Domain of Deneb, and granted the Ducal title to elevate him in order to enable him to hold the position? (Note that he was awarded a Lifetime TAS Membership from a world in Deneb Sector - perhaps to enable him to travel between Lishun and the Domain of Deneb?)
If so, you will want to make sure one of your sons is invested as a Steward or Seneschal of your Khalu Estates to oversee it in your absence and arrange to have its Moot votes given in Proxy to a trusted local noble in Lishun. It is fortunate that your sons were also both granted estates on Glisten so that they have places of residence should they choose to act as intermediaries between your current posting and your Khalu Estates.
Of course, the character concept is yours to do with as you please. Those are just some possibilities and suggestions.