If you have had no further criminal convictions in the meantime, then it might be worth trying again - the longer ago they are the more likely there are to decide they are no longer a problem.
However, travelling 'shortly' is unlikely to be on. In cases like this the London Embassy has to refer back to Washington for a waiver (of the requirement to reject applicants with a criminal record) and this can take several months.
I'd also say that attempting to travel under the visa waiver scheme is (for you) highly risky. They are almost certain to have a record of your visa refusal and you will have lied to them on two counts - saying no criminal record and no visa refusal - which will put back by many years any future chance of getting a visa.