Doing this for catchers was particularly simple for one reason. A player who played catcher tended to only play catcher. Once I moved on to looking at firstbasemen I had to decide how to deal with players who only played 1B occasionally or even just a few times. I decided to set a minimum of 30 games played at first base as a mariner as my cutoff. Its pretty low but actually worked pretty well. There were still tons of players who only occasionally played 1B or only played 1B for a couple of seasons. In order to account for this I looked up how many games the player has played at 1B vs how many games he had played elsewhere and only gave him credit for the fraction of games he played at 1B. Therefore if a player earned 10 WAR over his career and played 25% of his games at 1B he was credited with 2.5 1B weighted WAR. This might have its drawbacks but its simple to do and for most players I feel like it should even out. I also decided to do my WAR rate stat on the basis of PA since it is simple and straightforward even though defense is weighted per inning and it really just doesn't matter if I try more complicated stuff.
This first chart has all of the data for all the M's 1B for their WAR totals over their whole career. Olerud is clearly leading the pack and its not even close.
This second chart has all the information for the players while they were Mariners. Olerud is still in the lead with the highest raw WAR totals as well as highest WAR/PA numbers as a firstbaseman. Alvin Davis has a slightly higher total WAR total and higher peak year total but played far less at 1B than Olerud did. Tino Martinez, Bruce Bochte and Richie Sexson sort of round out the top 1B of the Mariners history however there is a large gap between these three and Olerud and Davis and a small gap between the rest of the pack below them.
The bottom of the list is dominated by some truly horrible performances by Dan Meyers and Pete O'Brien. Not only were these guys bad but they got lots of at bats somehow. Dan Meyers somehow had a season worth -3.2 WAR! This has to be one of the worst performances ever. Below average defense plus 477 PA of 227/264/327 is absolutely pathetic from 1B. (Oh my god, I just looked and the DH in 1978 did worse than this.) Bryan Lahair and Ben Broussard (sorry Jeff) are also near the bottom of the list.
Overall the Mariners 1B have produced ~50 WAR over the entire franchise's history which is worth about 1.5 WAR per season which is decent enough. Olerud and Davis represent about 60% of the overall franchise production from this position. I was surprised to see Olerud so high and had forgotten Davis had such a productive career. I don't know why but I thought Tino might be a little bit higher up on this list.
Best M's 1B of All Time: John Olerud
Worst M's 1B of All Time: Dan Meyers