Not only are there programs available, but there's many programs available.
When you say your income is too high for government programs, know that not all government programs have income limitations.
The only national mortgage products that have inome limitations are USDA and a conventional product offered by Fannie Mae and Freddie Mac called "My Community" and "Home Possible" respectively.
However, the caveat you may run across is the loan amount. If you put 10% down on $500k-$600k, you're over the $417k loan limit. There are higher loan limits for "High-Cost Counties", so you'll want to research to see if the county you're shopping in is a High-Cost County and what the loan limit is.
If HUD says you're in a high-cost county, you can put as little as 3.5% down on a FHA loan and FHA does NOT have an income limit.
If you qualify for a High-Cost County conventional loan (through Fannie Mae or Freddie Mac), you can also explore those options. If you do, remember that you'll need to qualify both for a conforming/conventinal High-Balance loan AND the Private Mortgage Insurance (Also known as PMI or MI). The PMI companies are more strict than in the past, so make sure your lender is familiar with each of the PMI companies guidelines. One of the most important things to look for in shopping a conventional High-Cost Conforming loan is which PMI companies your lender is approved with (or not approved with) and whether or not those companies consider your area a "declining market" area. If they do, the PMI companies would limit your maximum loan-to-value.
What this means is the lender may give you a loan at 90% but their PMI companies will not.
Sorry, lots of info given here, so if any of it seems confusing, just ask and I'll go more into detail.
The last option, which is more of a local option, is to see if any local credit unions or banks will offer a second mortgage above a traditional FHA, Fannie Mae or Freddie Mac loan up to 90%. Then you can get a first mortgage at $417k and get a second mortgage to cover the difference up to 90%. The large banks are hardly doing this, but some local credit unions and banks are doing this. The only exception to this may be US Bank or Key Bank, which both specialize in 2nd position mortgages, so they may do this for you. However, I have not heard Wells, B of A or Chase doing this.