For overall strategy, both of you needed more Advisors. It's rough that they can be Swindled into Death Cart...but it's also the only way to increase your handsize. Just cantrips is not enough to support playing as many Swindlers/Goons as you want per turn. Without Advisor, you have at most 5 cards in hand at a time, so once you account for having extra junk from Swindler and just okay trashing, you need hand size increasers bad.
Advisor + Cellar is the main way you can make sure you draw all your actions. The overall plan of Moneylender + Swinder early on is good, but I think you want Advisor > Mining Village early on, relying on your Necropolis and/or Squire for actions while you build up enough draw. You may want to consider getting more Squires - although you want to get actions from MV/BC only if you can, an early Squire can make Swindler risky, since if Swindler hits Squire, you gain a free Goons. Also combos with Death Cart if you're given one off Swindler. You definitely don't want to buy Death Cart here, but if they give it to you, might as well use it.