First of all create an inert atmofere to avoid air contact. Also, analyze inclusion you have. Than add some synthetic Slag on top of steel during melting.

Best regards

Henrique 

1- 5 um inclusion is not large inclusion.

2- Deoxidize the steel melt by Aluminum (0.08%wt%) and then modifies it by Ca addition (1wt.% Ca-Si powder 70-30). this can be done on the ladle. Amount of Si and C are important. Please read the chemistry of steelmaking (Deoxidation and modification of inclusion)

3- Non metallic inclusion larger then 30um are exogenous inclusions that are very hazardous for forging and rolling processes.

In general the inclusions are oxides. I think you need to use the vacuum induction furnace.

Inclusions are Fe Mn sulphides.

It is necessary to reduce the content of sulfur in the alloy. This is a hard case in the foundry.  In the steels is important to use pure alloying.

what is the effect of Al, Ca and Zinc if retained in austenitic stainless steel on mechanical properties?

It is difficult to remove inclusion completely from steel. you can produce clean steel only under vacuum or inert atmosphere. Since the inclusion you found are Fe-Mn sulfide. These inclusion are elongated or streak type which would affect the mach inability. So i would say that by adding Ca, Te,Zr, Ta, Ce, you can modify the morphology of the inclusion but to completely avoid it you need to get some experience on steel melting process control parameters like super heat, liquidus temperature etc.

 for super clean steel, ESR (Electro slag refining) process is required to remove of large sulfide inclusion and modifies remained oxides and sulfides inclusion to small sizes and non-deformable oxisulfide inclusions in next forging or rolling process.

for meduim or experimental size of steelmaking, you need low sulfur scrap or ingot and you must be control of atmosphere and lining of furnace and ladle (basic lining is required)