Refer me to help documentation if I should be finding this in there....but is there an easy way to drop a saved search into a custom UI form (that I am creating in a Suitelet) and filter it by a transaction internal ID?  

It seems that you can do it like this:
  [h=2]

setLineItemValues(values)[/h]  Sets values for multiple lines (Array of nlobjSearchResult objects or name/value pair Arrays) in a sublist.
  [h=5]Parameters[/h]
[LIST]
[*]values {nlobjSearchResult[] | hashtable<string, string>[]} [required] - An Array of Arrays containing name/value pairs containing column values for multiple rows -or- an Array of