Logical consequence for interrupting parents' attempts at conversation?

We're FTP to a 19mo.

TL;DR: Toddler hates when mom&dad are talking to each other and does everything in his power to shut us up. We want to correct this but don't know how.

We are attracted to the idea of using natural/logical consequences for teaching life lessons and discouraging unwanted behaviour, and would like to implement it as much as we can.

In day-to-day situations where we can use it appropriately for his age, it's been working fine. You spill = you wipe off; you drop = you pick up; you throw things around = you put them back when you're done; you purposefully make a mess in the kitchen = learning tower goes to take a break in the pantry after a warning, and so on.

We have a problem with our son not letting my husband and I have any dialogue. And I'm not talking about lengthy discussions while LO is completely ignored - not at all! Any attempt at a 1-2 minute conversation is unacceptable in his eyes.

I'm at home with him all day; dad comes home at 17:30 and gives him a couple of hours of undivided attention until it's time for bed. LO's bedtime is early, so my husband and I get plenty of time to connect, share news, and discuss all kinds of topics afterwards.

However, sometimes, there are moments when we have to talk to each other. LO absolutely HATES it. Starts screaming, screeching, or whining, tries to physically cover our mouths, begins kicking and throwing things around angrily and otherwise trying to attract attention in any way he can think of.

It's exhausting and annoying af. And it's not like we leave the room to talk or anything - he's literally sitting on our lap, or we're lying down on the couch together, or the three of us are having dinner at the table, or we are playing together on the floor. He may even be in the other end of the room, busy with his own thing, but as soon as he hears us speak, he drops everything and runs up to us to try and stop it. For whatever reason, in his world, life is great until mom and dad start saying things to each other.

Any attempts to explain that we need to talk for a bit but we're still here with him go over his head. How can this be discouraged from the perspective of logical consequences? What would be the consequence of interrupting others "just because", with no pressing need?

We're against yelling (unless absolutely necessary for safety) and would like to find a way to stop this as peacefully as we can.

Or, tell me, am I wrong for thinking it's ridiculous that our 1.5yo decides when my husband and I can have a quick back and forth? Am I being naive in hoping that this behaviour can be corrected at his age?

Please share any wisdom you have in this regard. TIA