I definitely agree that your issue was distribution. I'll share my experiences here, because I have the same E37s grinder, and I also use an Aso Jack leveler. This is what works for me, but it's not fully in line with what others have suggested. So YMMV.
- I grind directly into the basket, and I don't do anything special - no shaking, no rotating, etc.
- Using a dosing funnel, I do a pretty vigorous WDT, but I'm using a rather thick metal probe, around 2.5-3mm thick.
- I then use the leveler to smooth the puck and lightly compress it. If the grounds are particularly uneven after my WDT, I'll first spin the leveler while holding it a little above the rim of the basket, then repeat with it fully set into the basket.
- Then I pull my shot - no tamper used. And I get pretty consistent results - 18g in:36g out in 25-30 seconds, and more importantly it tastes good.
- I brew primarily medium to medium-dark roasted Italian style beans, such as Caffe Lusso GCM or Stumptown Hairbender. If you are pulling shots of some lightly roasted African varietal it may not work the same
- This was on my E61 machine, and i'm not using it at the moment. I'm trying to get my shots perfect on my manual Cremina, and I don't have a distributor sized for that basket yet, so I'm struggling a bit myself with that machine
Anyway, good luck working through the issues, and I'm sure you'll find the E37s is up to the challenge.