no i don't think the issue is the inks - but rather the roller that grabs the paper. it should not be making marks unless it is having trouble feeding the paper. have you tried assisting it in - or getting above it to watch if it is able to grab it right away or it needs to roll a bit and that is causing the marks. the age of the printer is not what usually makes for a dirty roller - rather it is paper lint. if you always use epson inkjet paper this is rarely a problem. if you use any of the fine art grades of paper they will leave lint.
there always remains the possibility that your R3000 is just extremely aggressive in its paper handling and will always do this - but it may be worthwhile assisting the paper in by hand in case it's leading edge is getting hung up on the thin plastic trim that prevents additional sheets from falling in when a sheet loads. You should be able to see if that is happening by observing when the paper loads. If it does not take it instantly, that roller is going to dig at it until it does.
Have you observed this area during the load operation>