Yes, another employer can file a cap-exempt petition for you within 6 years of original H-1B start date. There is a blog post on main site where someone has explained their successful experience w/ this.
This is slightly grey area. As you had H1B stamping done, you would be considered cap exempt as you had H1B status at least once. if you have an employer willing to hire you, they can use the details and apply as cap exempt. Also, the 6 year rule does not apply anymore. Read H1B Time Recapture Rule