Originally Posted by George Mann
It sounds like you may be looking for the Fender Original ('62) replacement pickup.
This^^^...the 62 Originals aren't as "hot" as the DP's and will get you much closer to a classic Precision tone. The DiMarzio is kind of a step in the opposite direction...more modern sounding and approaching an "active" type of split coil voicing. Lindy Fralin stock wind is also another great option but pricier than the Fender.
Official Fender Precision Bass Club #881, Gallien Krueger Official Club #921, N.Y. Bassists Club #52