Can I ask what grind you're using? I'm a big fan of the bitterness of what my moka pot produces, though I agree that it's not "espresso" per se. It's fantastic for mixing with vanilla ice cream or mixed drinks.
Espresso grind (fine). Just slightly finer than I grind for using in an Aeropress. To give an idea, my grinder scale is 1-34. I use 1 for Turkish, she likes 5 in the Moka, I use 6 in my Aeropress. Drip is ~12. French press is ~18.