Exactly as Slobodan says... you're messing up your color management by telling Lightroom the printer is managing colors; while at the same time you're telling the print driver that Lightroom is managing it. It's a classic mistake and inevitably leads to poor results.
You have two ways you can go...
If you want to let the printer manage colors, leave your first dialog as it is ("Managed by Printer" under 'Color Management'); then in the subsequent printer dialog, go to COLOR MATCHING and select "Epson Color Controls").
Or, you can use the method preferred by most serious printers and use profiles. In that case you'll need to go into that first LR dialog, and under 'Color Management' click on the up/down arrow mark just to the right of "Managed by Printer." That will give you a drop-down of all your available profiles. Select the appropriate one. In your case it will probably be something like SC-P600 Series Premium Photo Paper Glossy.
Either method will give you pretty good results. The second is more predicable and controllable, which is why it is generally preferred.
A couple other quick thoughts...
Soft-proofing implies use of a profile. That means the second method.
If your prints are still too dark, it's probably because your monitor is set to a too-bright luminance level.
Welcome to the forum!