A key thing in this type of scenario is to build the tree as wide and deep as possible, bring it towards the present day and have as many descendants as possible test. Knowing how much dna everyone shares with everyone else (not just what they share with you), may point to half relationships in some cases which were previously unknown. The problem however is that the relationships are quite distant so not everyone may appear as a match and the shared dna figures of matches could apply to full or half relationships in some cases with no way to be sure which is correct.
I've had a result come back for a paper trail full 1c but the cM figure is too far low, at best we are h1c. When taking into account other matches in that part of my tree it's apparent the children registered to my grandparents are not all full siblings to each other and it's my line that is the 'half'. Were it not for that one test I would be none the wiser as the others are at least one and sometimes two generations further along so the shared cM amounts are less conclusive. I also have some matches between 200-280cM that are unique to me which I can now be more confident are in the 'missing' part of my tree.