EPL has the restriction that if you distribute binaries, you have to make the source available (you must state in your license where to obtain it). It seems that listing your dependencies libraries and linking to their websites (which I think is good practice anyway even with less restrictive licenses) would be enough, as long as you didn’t modify them.
EPL allows linked modules to be distributed under whatever license you want, so in a commercial product doesn’t apply to your closed source code or any libraries that choose not to be distributed under EPL.
So for on prem distribution, you just need to include a license file that lists all of your EPL (or other licenses that require the license to be included like MIT) with a link to where to get the code. Your own code is unaffected.
This isn’t GPL compatible, though, because GPL does “infect” linked modules too.
However IANAL.