It's tough to find a balance here. If farming gets you more value, there's less interaction. You just don't see the jungler for fifteen minutes, then they come out of the jungle fed. At least with ganking junglers, you have a chance to deny them that kill and have some input in the situation.
I think adjusting the gold and XP scaling for the jungle would be a great place to start. Maybe make the first spawn of jungle camps worth a lot more gold, but that extra gold only lasts for a few minutes, kinda like plating. There could simply be more jungle monsters in that first spawn, or one or two "roaming" camps that wander around your side of the map. This increases the time it takes to do the first clear with good incentives for the jungler to stay in the jungle, so laners have more time to interact with each other without worrying about an early gank. Junglers would still get opportunities to gank, they'd just be a bit later in the game when things are a bit more established.
I think towers should also be scarier for the enemy. There's no reason why towerdiving for anything other than the last hit should be a thing. No champion should be able to just live under your tower, fight you, and win. Armor penetration/mixed damage or an on-hit effect like a slow or mini-silence would be great ways to improve the threat of towers.