First, I agree with all decisions hero made except with an open sizing to 4x; I would default with a 5x at these stakes and potentially make it 6x or 7x depending on how the table reacts.
The most important consideration to make in this situation is pot geometry. In this situation specifically, pot geometry can translate to "how do I get all the money in". While you could go with a near pot size bet on the flop, I think this is a poor decision because your hand will be completely faceup to any competent opponent, with the absolute bottom of your range being AdKd.
If you make it a smaller size like $50-$60, you leave yourself plenty of room to get stacks in on the turn when villain has a hand that will pay you off, and you capitalize on the times villain is out of line with something like 78s or a flush draw. Potting the flop will most likely force middle pairs and flush draws to fold.
Imagine how the rest of the hand plays out when you pot the flop. The pot becomes $330, with ~$50 effective behind, which means you basically told everyone that you are committed to your hand. No player alive will fold to a $50 turn shove.
Now imagine what it looks like when you bet $60. The pot becomes $230, with ~$90 effective behind. Villain will be forced to call a decent chunk of his range on the flop, and will have to make a difficult decision when you shove turn.
If you couldn't already tell by the tone of this answer thus far, doing anything but betting is not an option at these stakes. If villain has a hand that beats us, so be it. Assuming he doesn't get out of line (which is probably not true), he stacks us when he has exactly AA or JJ, and we get his stack when he has AdXd, QQ, and depending on what he range looks like he might have things like AJ or JT, which will at least pay off your flop cbet.
My general strat in 4bet pots on Jd 7s 3d:
If I am playing an unknown or someone I perceive to be a weaker player, I will cbet around 50% of pot with all top pair+ hands along with AdKd/AdQd, and check fold everything else.
If I am playing a player I feel is capable of folding AJ, I will add AdX to my cbet bluffing range and bluff shove of most turns, for the sake of being balanced.
The above strategies assume that the pot geometry will play out the same as in Hero's scenario.
Also, if this is your first time hearing the term pot geometry, I would strongly recommend checking out this article and video.