My awesome position:
I wouldn’t run here because you aren’t really up in the race after the roll and if you get hit you lose your (small) racing advantage. You also let White have all the initiative with lots of good things to do.
Looking for other plays, my mind goes to Michy’s proverb “fight for a good point” here. Like you mentioned you really don’t want White to make your 4-point and, although scary, you have a lot to gain; any of White’s 9 fanning numbers make you a big favorite and get you a cube. If you get hit, you are likely to get an anchor and should have plenty of game left.
Admittedly I would question my own judgement here over the board and take my time to think it through, as breaking the 7 and 8-points to hit seems bold.
Tempo is a big part of it. Notice that with a 3-point board, your opponent stays on the bar 25% of the time and forfeits their whole roll. And then you can double. If there is a sequence after a play that gives you a double, that usually means that play has the highest equity (i.e. is correct).
Putting your opponent on the bar while making a new inner-board point is always powerful. So don’t get too attached to an outside prime; look for opportunities to roll it forward on their head.
(A little redundant with what hemes said, but I like to put my ideas down before I read others’.)