This is not professional or technical advice - only opinion.
Consider:
1. original specification?;
2. weight;
3. ability to hold screws, and;
4. what forces the original beam had to contend with(prodder?)
I think your beam would weigh about 16kg at 4m (380kg per m^3), whereas you could make a hollow one as per plan for about 5kg less. WRC also absorbs resin more readily than for example oregan pine, making a sheated beam heavier. WRC does not hold screws very well and if you want to screw the fastners for the net into this then you will run into trouble.
Also consider rigidity. Depending on how the original box section is designed your western red cedar beam could flex differently. This may or may not be good.
I prefer to use Western Red Cedar as core material for composite components, and dont use it for structural components on it's own.
Sincerely
John H