Lol.. you have so many misconceptions it isn't funny. The minimum wage was created to curb minority companies under bidding bloated established white companies. It created a base level that barred those willing to work for less from taking well paying jobs. Mandating a prevailing wage in government contracts was much the same. In more modern times, the minimum had been used to stealth tax increases as both the employee and the employer has taxes associated with pay that does not get refunded.
Second, union busting has never been popular in recent times. People started seeing unions in a negetive light when Reagan busted the air traffic controllers specifically because they walked off the job and left people in danger in planes in the air with no one directing their movements in a reletively tight airspace. That is when people started seeing that 90% of what unions were needed for was already encoded into law and their remaining usefulness was mostly about greed of income. But what really killed the unions was downsizing in the 80s where the bloat was consolidated and made efficient. This lead to companies poping up that could compete far better than most established union shops and they took an even deeper hit with the offshoring craze that pitted union wages against third world wages. Outside of the traffic controllers showing how wreckless the pursuit of greed can be, it had little to do with the fall of the unions.
As for income inequality, the majority of the income being considered too large is performance based. It is stock options, bonuses and so one attached to a base pay. It was originally done this way in order to shirk pay obligations if the executive failed to properly run the company (with some tax strategy). The problem is it an incentive to keep wages low and stagnant. It isn't so much the inequal amounts that is the effective problem but what makes those amounts so inequal. Now i know you are looking at fixing it meaning increasing worker pay but the realities will likely be decreasing exec pay and simply giving them prefered stock where they get the same but it is counted as dividends separate from their pay.
The only way to fix this is to tie employee wages to the same or similar bonus structures. This way, even if the ceo makes 20,000 times more than the base hourly pay for workers, those workers get rewarded the same. I have seen people who actually do get profit sharing earn as much as 2 times thier anual salary fron the profit. Mostly it seems to be one third to two thirds more.