I am going to break my thoughts into several posts because the topics being discussed are complicated; they are related but somewhat different.
This post is about using diploid pollen on tetraploid pod parents and using tetraploid pollen on diploid pod parents.
If you do those pollinations they will appear to work just as often as the diploid pollen on diploid pod parent and tetraploid pollen on tetraploid pod parent ones work.
Pods will be set and will start to develop.
By ten days after pollination (dap) most of those pods will abort. By thirty-five dap nearly all of those pods will have aborted. A few pods will mature. Most of those will have no viable seeds even if the seeds look good. A very few seeds will be able to sprout and produce seedlings. Toru Arisumi did the studies and found that any seedlings produced were nearly always triploids. I can look up the exact numbers if anyone wants specifics but going by memory it was 1 triploid seedling for every 50 pollinations (dip x tet or tet x dip). Not all crosses produced pods that lasted for even one week - the numbers are biased towards those combinations of parents that set pods that lasted for at least one week.
Maurice