This is sort of the problem w/ Dianna jungle in general. The reason early game jungles are prioritized so much in pro play is bc coordination is high enough at that level to punish "lvl 6" jungles in general. One thing you can do (I'm bad at this myself which is why I'm struggling a bit since switching to main jg again) is to watch your lanes and how they're doing during your early clears. If some lanes are struggling and you're worried they're going to get behind you don't need to get a kill on a gank for it to be worth it. Chunking the enemy down so your lane can get some cs while the enemy backs and then your lane can back w/ the same cs as the enemy for even first buys instead of being way down after first buy can be a huge thing when it comes to keeping your lane from feeding before you it six. Similarly, if you blow a flash from the enemy laner, you can come back for the kill later, or power farm to six while your laner uses flash advantage to make the enemy play safer (your lane can escape but the enemy can't so a bad trade for the enemy is worse than a bad trade for your teammate in terms of kill potential when they back out and get their cd's back up after the trade).
Other than that your only real option is to be proactive about warding and hope your lanes are only going to feed to jungle pressure rather than just vs their lane (ie use your trinket for top lane as theirs expires by warding over the ledge/walking down depending on the side if you've cleared top jg and are backing due to low health, and buy a green ward on first and second backs if you can so you can ward for lanes if you aren't putting out pressure w/ your ganks). Also you need to put down enough pressure w/ your lvl 6 it makes up for your lack of pressure early. I am not a particularly good ww, but a good ww should basically ALWAYS get a kill w/ their first ult gank. It sets the lane ahead or catches them back up if they got behind while you power farmed. If bot gets ganked a couple times and gives up a kill or two, you can reset it at lvl 6 w/ amumu ult killing both enemy adc and support. I don't play a lot of Dianna, but if I know the match up right, at 6 she wins almost every 2v2 if her lane isn't super behind, in games where it's even this needs to become a huge advantage. Instead of just getting a kill w/ the gank, getting a double kill by counter ganking the enemy jungle not only gets double the gold for your team, but also stops the enemy jungle from having influence past their early game influence. If you do that consistently then you have a huge advantage in games where your team doesn't feed early and it may bring your win rate in other games up so that the games your team feeds in all 3 lanes don't hurt you as much. (If one lane feeds but others are even, then it depends on if the jg just camps the lane that is ahead or tries to get the other lanes ahead too. If they do the latter you can counter and then you have 2 lanes ahead and one behind, so you can roam w/ one of the lanes that is ahead to get the other lane back in it bc you have more total power than 1 fed laner.)