Martin -
There were a couple mid-line large capacity Whirlpools from the mid 80s that had those knobs. Oddly, this was the full-line console style in 1982-1984 or so, just as you said, but certain models continued with it with the 1985 models, and some higher-ups got the more woodgrain fully sloped console.
I bought an LA5580XP in summer 1986 at Circuit City before I found my Kenmores on sale. The washer looked identical to this - was a large cap and the dryer standard, but that was how they were selling the pair. You're very right about the dryer...I am not sure any large cap. versions had the side-swing door. The washer had a winged Surgilator, and yes indeed, a manual filter...Whirlpool was big on them up to the end of the belt-drives while Kenmore had dropped them years earlier.
Nicely featured machine, if I remember correctly it had four levels, three temps (or that may have been reversed), two speeds, four cycles. Other than the lint filter, which I thought was AWESOME, there'd be nothing to object to for any consumer, but many didn't like manual filters. There was one model lower, which eliminated one of the levels/temps that also looked similar. My pair was going to be Toast in color, it was either that or Almond so I picked Toast. I really wanted the KMs though, but I have wondered what would have been had I taken delivery of the WPs.
Funny about the ad!
Gordon