maybe go see an accountant who can look at all your financial details and give you professional advice
+1, you should really get professional advice on this...
I can't pretend to know too much about this, but this is how I understand it. Assuming you and your husband are under 50 years old, then you can each contribute $5,000 to an IRA which if you are married filling joint would reduce your AGI by $10,000. Being as only your income is on the books, then you would contribute $5,000 to a personal IRA and $5,000 to a Spousal IRA for your husband (you can only contribute to an IRA up to the amount that you have as earned income). If you take a distribution before the age of 59 1/2, the taxable portion of the distribution will be penalized by 10% (in your case the whole amount) on top of the regular taxes you would owe. You are be able to take a distribution of up to a maximum of $10,000 per lifetime per person as a "First-Time Home Buyer" and you would not be penalized with the 10% penalty for distributions before the age of 59 1/2 but you would obviously have to pay taxes on the money that year as you took a deduction when you contributed originally.
Now AFAIK non of this actually helps you in this case because the EIC limit is on both Earned Income and AGI...
Can't think of any way to actually lower "Earned Income", but then again I am a programmer not an accountant