I've been working on converting my 1995 Trek Mountain Track from canti to v brake and ran into the same problem. There are heaps of guides online show you how to swap the brakes and levers but nothing about the cable routing, so I made a short clip of cutting mine frame to test, this is the cleanest way I found without adding cable stop clamps etc...and it works.
https://youtu.be/hEF09cKdb0Q
i've done something very similar to clean up a mess made by a customer during an "upgrade". You did fine. My cable housing adapter was from an old cannondale, if i recall correctly... and the "mess" was on a very similar Trek MTB... it involved a hose clamp over duct tape, and kept slipping.