FWIW, there is some discussion of changing the law to ignore investment income for EITC. Who knows if it will pass or not.
A couple of thoughts:
If you sell your taxable investments, you'll probably have capital gains that year that exceed the EITC, so no EITC that year for you.
You could try to funnel the money over time into your Roth IRAs (including your spouse's if you're married), or your workplace retirement plans. Do you have a 401(k) or anything like that available to you?
You could gift money to your kids, which would shift that income to your kids and get it off your tax return. I don't believe EITC would look at their returns. But the kiddie tax may affect this effort.
You could open 529 plans for your kids, which would get the income off your return.
There are individual stocks that don't pay dividends. BRK.B is probably the most well known, but a lot of tech stocks could be included in that list.
Rental real estate might work. I'm not sure if rental income is considered investment income or not for EITC.
...
Or you could just give up and be a high-income person that EITC isn't really intended to target. Yes, it's a juicy tax benefit, but it's intended for low income working families. I've looked at trying to get it in the past when my circumstances were different, but the contortions I would have to go through to get the credit would have damaged my financial wellbeing more than the credit was worth.
If you're still going to try anyway, note that even once you manage to qualify, there are limits based on two different things (AGI and earned income I think) and you get the lower of the two amounts. Also note that claiming EITC will delay any refund you might get until mid-February, and also probably increases the probability of your return being audited. Finally, if you claim the EITC but were not entitled to do so, there is some lockout stuff that the IRS can do if you try to claim it again later (possibly legitimately).