OP: It sounds like your “senior” design engineer is an old graybeard who walks around grumbling and mumbling to himself about “…in the old days we used to lay out boards with tape and markers…”
How can anyone with any CAD experience in schematic capture and PCB layout – assuming the old fart has actually designed stuff in the last 20 years – find a rat’s nest “weird”?
It sounds like you’re pretty much stuck using Protel if this is what the old graybeard demands so fire it up and take it for a spin. Sorry I can’t offer specific Protel info (I use Altium now and Cadstar before that…) but can’t imagine any such package not offering a rat’s nest for visual assistance in component placement and interconnections.