To return to your original question:
As @thumper1 and @politeperson noted earlier, the 2-year lookback is based on the academic year, regardless of when you actually file taxes or FA forms. So:
Academic year 22-23 Fr (income from 2020)
Academic year 23-24 So (income from 2021)
Academic year 24-25 Jr (income from 2022)
Academic year 25-26 Sr (income from 2023)
Money contributed to a Roth is not reported to colleges as untaxed income (or any type of income), because it is after tax.
It is reported as a retirement asset, but it is intermingled with your other retirement assets (if any) when reporting them and colleges say they do not assess against retirement savings. So they will know about it, but have promised not to “use” it.
Note that if you already contribute to a regular IRA, then there are rules about how much (if any) you can contribute to a Roth. There are also income limits, but based on what you reported earlier, I don’t think you exceed them.
This is my understanding: If no other restrictions apply, you can put 6k each year in a Roth for yourself (7k if over age 50) and your spouse (if any) can do the same. As for your kids, they can also have a Roth if they have earned income (they can contribute up to their earned income, not to exceed 6k. You can use your HE funds for their Roths on their behalf – they don’t have to use their own actual income).
Thus, it could play out like this:
Jan 2022 or later: home equity funds dispersed
Set aside what is needed for AY 22-23 tuition
Make your 2021 Roth contributions by April 15, 2022
Make your 2022 Roth contributions any time in 2022 (but before you file FA forms for AY 23-24)
August 2022 (likely): Pay tuition for Fall 2022
January 1, 2023: Contribute to your Roths for 2023
January, 2023: Pay tuition for Spring 2023. Pay any other big expenses.
Jan-Feb 2023: Fill out FA forms for AY 23-24 (check school deadlines, as they vary)
For the FA forms you fill out in Jan/Feb 2023, your assets are increased by whatever is remaining from the Home Equity loan, but decreased by 3 years of Roth contributions if you time it right (2021, 2022 and 2023) – so 26k or 42k assuming two parents, depending on ages and some amount for kids.
August 2023: Pay tuition Fall 2023
You can then withdraw money from the Roths anytime after January of 2024, since that is later than your latest “lookback” period.
Roth monies are categorized as both contributions and earnings, and different withdrawal rules apply.
Withdrawing your contribution is always penalty free and tax free.
Withdrawing your earnings is tax free and penalty free if you withdraw after age 59 ½ and have had the Roth for at least 5 years.
Withdrawing your earnings is penalty-free but not tax free if you withdraw before 5 years of Roth existence, regardless of age, if they are used for a qualified educational expense.
Note that if your kids are taking a gap year, then all of the above dates get moved up by a year, and it also gives you one extra year of Roth contributions before you start the withdrawal.
Also note to of course check with your accountant or other professional about tax matters – this is just what I have learned for myself.