the type does not change when carried forward. however, there is an order to how current year gains are applied
first the current year type of gain is applied to that type of CLCO. so short term gains are applied to ST CLCO and long term gains are applied to LT CLCO.
then if both types are still net losses ST are used first against regular income up to $3000. if one is a loss and one a gain the loss type is applied to the gain type.
so in your situation for the current year you have net STCG of $500 and $500 of LTCL
thus the LTCL is applied against the STCG resulting in a net of zero