I see the point -- and I believe the meaning of the data involved is slightly more nuanced. This is TL;DR -- but intended to limn the technical situation.
DEVONthink records have four date properties: creation date, addition date, modification date, and opening date -- which are, respectively: the date the document was created, the date it was added to the database, the date is was last modified, and the date it was last opened in a tab or window. Generally these are the same "created" and "modified" properties that the file system tracks and Finder, for example, can portray. All of these DEVONthink date proerties, but the last, can be modified by scripts. (Why this is possible has a long and odd history.) There is no "due date" property for DEVONthink records.
When Tinderbox creates a note from a dragged in record from DEVONthink there is no $DueDate, $StartDate or $EndDate data anywhere in DEVONthink that could populate those attributes. Tinderbox has its own $Created and $Modified attributes which are read-only -- and relate to that note and not to properties of the source data. They are similar to but different from DEVONthink's creation date and modification date properties.
So, the suggestion @andreas makes would be constrained by the non-existence of event data (calendar entries or reminders) in DEVONthink 2.x, thus far. It might be better, if feasible, for creation date and modification date from the DEVONthink record to be mapped to some other attributes -- perhaps if Tinderbox made something like $SourceCreated and $SourceModified attributes for imports and populated them as @andreas suggested?
I suggest these generic terms to accommodate "fetching" from other sources. BibDesk imports already have their own dates in the References set of system attributes.