Purpose of the conversion of 3-PGA to G3P in the calvin cycle?
Nice question! To see what trouble that extra oxygen can cause, lets get to the core of the reaction i.e. Calvin-Benson cycle; one step at a time. To start with, have a look at the detailed Calvin-Benson cycle (following image taken from here):



As becomes quite clear from this image, the actual use of Glyceraldehyde-3-phosphate is at the step of formation of Fructose-1,6-bisphosphate. Yet, we don't know why we cannot use 3-Phosphoglycerate instead at this step. For that, lets go a step further and see how the concerned enzyme, fructose-1,6-bisphosphate aldolase/phosphatase (aka aldolase), works.

Since the full article is behind a paywall, lets get a sneak peak into it. See this image1:



Pay attention to the steps where G3P enters i.e. steps between b and c. Even without entering into details of the mechanism, we get two factors which can prevent 3PGA from being utilized in this reaction:


Steric Hindrance: replace the terminal -H with -OH of G3P in the first image in your mind. You can clearly see that this would cause some steric hindrance and prevent formation of covalent bond between DHAP and G3P.
Formation of Geminal Diol: again, replace the terminal -H with -OH, but this time in the second image, in your mind. You get geminal diol in the resultant molecule, which is famous for its reactivity and instability. Thus, by adding 3-PGA instead of G3P in the reaction, we might end up with unstable molecules that cleave themselves up. I hope this is what you were looking for.


Reference: Juan Du, Rafael F. Say, Wei Lü, Georg Fuchs, Oliver Einsle Active-site remodelling in the bifunctional fructose-1,6-bisphosphate aldolase/phosphatase Nature 478, pages 534–537 (27 October 2011)
doi:10.1038/nature10458