Sorry, but you are out of luck. If your salary is high enough that you are an HCE, then you are beyond the limits for having a deductible IRA. You can still make a non-deductible contribution and then immediately convert it to a Roth IRA. You'll pay the full income tax due on the amount you put in the Roth, but at least it will grow tax free.
The HCE tests and limits are put in place by the IRS to ensure that 401Ks are not disproportionately benefiting people who get paid more while excluding those who get paid less. Since the earnings threshold for HCEs has not kept up with salary growth over the years, and since it was never really reasonable for some industries or some hcol locales anyway, the rules really just end up preventing a lot of middle tier earners from saving as much as they want to.
There are three things you can do to make the 401K fully available to you again, but none of them are really practical:
- try to get more of the non-HCEs you work with to contribute
- convince your company to provide additional matching or direct contributions for the lower earners
- if you are just barely over the HCE threshold and don't anticipate having a salary increase again in the next year or two, then you can offer to take a pay cut that puts you below the limit in exchange for an extra day or two of vacation time