I could be wrong, but... I'd be leery about using something like lacquer thinner on a vinyl dash pad, because I think it would be VERY likely to attack/harm the vinyl. At the very least, try finding a similar vinyl-trimmed upholstery piece (cheap/trashed) in a junkyard, spray it with the same dye you used on the dash pads so as to achieve the same rough result, and then experiment some with it before trying anything on the pads.
It sounds as though you might have sprayed the dye on from too great a distance, and it dried too much before it hit the dash pad.
Perhaps using a vinyl cleaner and buffing it might help, but frankly I really don't know for sure how you can recover from the current situation... you might try asking a local upholstery shop, or try to contact the maker of the dye that you used to see if there is a dye thinner you could spray or gently rub on that would help smooth the surface.