As the others have said, the stats do carry forward through the rest of the relic upgrades. I did full Crit and Det on my first one (bow) but for the second (blm) I didn't bother with any Tier IV's at all.

The first time around, it took quite a while to do this because of the time it takes to get Alexandrite. I was making money by SB'ing crafting materia. When I got a tier IV, I'd sell it and buy one that I needed, watched prices on the MBs to get the best deals, etc. For my second, I already had all the Alexandrite so just slammed it once I cleared the books stage.

Second time was also a bit easier because the Zodiac quests can be repeated - you can get lights for the Nexus stage while farming dungeons for the Zodiac turn-ins.