I think image peocessor pro may be able to do that
No actually I need action i will try but not succeed
The image processor pro is a plug-in you can record using it in an action.
You can do it with action and batch.
EPS is opened as new document with width exactly 4000px and height is computed proportionaly. After opening one of your side will have 4000px
File > Automate > Fit Image has max-height and max-width 4000px. This command decrease image if height is bigger than 4000px and constrains proportions.
And finaly you will save your file as PNG.
Remember, you need override open and save command in batch dialog and select action in batch dialog.
When you drag EPS in Photoshop above tabs: