shoving against early position aggressive player

against a early position raise, my kj suited was not strong enough to rejam with 20 bb; (I would rejam against a later position opener ); so I just call the min raise; I flop an open end straight; back door flush and 2 overs and I have 2 good blockers to the nut straight; my thought was to check raise(jam) the c bet, but villian just checks the flop; I now get the top pair on the turn with k kicker and still open end straight draw; I checked the turn and there is a small bet from villian; so my thinking was I have the king blocker to his potential kq; and I have a J blocker to his potential suited JQ;   he could of course  have AQ; I decided to represent the straight and check raised  all in;  but now thinking about my move I think I should have just called his turn bet; as what hands would he fold that I want him to fold by jamming the turn? He calls with straights; he probably calls with 2 pairs; he might even still call with AJ; ; so I think my jam was a mistake;  He actually called  with pocket jacks; If Hero just calls  the bet turn and then if there is a river blank; and Hero checks the river  and Villian shoves; would you have called the shove for your stack as at this point given my stack size am I not committed anyways? How would you have played this one,? thanks, Tim