Keep them as state corps I would say. I am biased, I like state corps in the main, most I can make pay more than private (CRU) anyway, contrary to popular opinion banded about the forums.
When you sell the 15% of shares, like you have done in your publics, all you really have done is received a one time payment for those shares and now that 15% of profit will go to some other entity every month.
If you have or plan on getting an enterprise then you can use the IPOing tool quite successfully by sharing the shares between country and enterprise and this also allows you to upgrade your corps further (to 225 initially) and so make higher Q products or the same Q products with cheaper supplies. It increases profit done right.
Without an ent' you are just selling your future by random IPOing.