Current EU investor is saying it will be a “down round” if we raise a round on lower valuation than latest cap. Anyone having a good method of communication to mitigate that assumption?

If the new round is a priced round, remember a note/safe cap is the “maximum” an investor is willing to pay for their percentage so you don’t really need to consider it a down round as the cap is not the actual post-money valuation. You can even have an uncapped note (i.e. infinite cap) and then price at $xxM creating a de facto down round. If it is a secondary note/safe, there are other tricks you can leverage such as advisory shares or warrants that brings down the “effective” cap while maintaining the same or higher cap on the safe/note.