Ok, Sol, we are in the situation you are considering. Well, with different details, the largest being that we are not yet near enough to FIRE.
We paid off our mortgage early, but it was a no-brainer for us, the rate was 9.75%. We have never been high earners, so we didn't have a taxable account to liquidate, we actually used our decent sized tax refunds from EITC and CTC to make large lump payments every year. We weren't saving much in retirement accounts at that point, just 5% in DH's to get the match. When they did away with the match, DH wanted to quit contributing, but I tweaked his withholdings and doubled his contribution to 10% with little change in take home pay. That showed me how pre-tax contributions increased our EITC (actually, lowered the phaseout), so I kept finding excuses to increase his 401k contributions: paid off student loans, I began working part-time, etc. When we reached the point where we could just raid savings to kill the last $10k on the mortgage, our oldest DD1 was beginning college. Ultimately we decided to hold onto that $10k in case we needed it for college expenses, and pay the mortgage normally to a a year to see how things shook out. No unexpected college costs, and we paid the mortgage off fifteen years early, and I bumped DH's 401k contributions up to 40+% of his pay, while agreeing that he could stop working summers. Also opened Roths for both of us, funded by our tax refunds now. As my part-time pay increased, I increased his 401k contributions to over 50%, finally maxing it out.
Our state matches the EITC at 30%, and the CTC at 33% (for kids over 4), so reducing our AGI is even more beneficial to us.
Look closely at the FAFSA rules for the simplified needs test and auto EFC = 0. There are two parts to the test, the AGI section PLUS another test you need to meet to qualify. Being eligible to file a 1040EZ or 1040A will work, but I have a feeling many mustachians must file a 1040 for some reason or other (we do since we have an HSA). Other qualifiers include receiving free reduced school lunches (that's our qualification), SNAP, TANF, etc. The rules and income charts change every year. We were easily eligible for auto EFC = 0 when DD1 began college, but by the time DS2 joined her the threshold had been retroactively dropped from $32k to $23k AGI. I've watched the income protection chart shrink every year since 2008 when DD1 began - the figures should be larger, not smaller, due to inflation! Luckily, the majority of our stash is in retirement accounts (effectively invisible, to the FAFSA) so our assets haven't been part of the EFC formula, so far.
Financial aid is complex, though. The fafsa is just the so called Federal Methodology, for federal aid. Each college also has its own Institutional Methodology, as well, and that can include anything they want to consider for handing out their scholarships and grants. They can consider home equity, if they want. Each college is different, and just because you have an EFC = 0 does not mean they won't gap you - or just tell you to take loans. Our kids have chosen schools that given them scholarships, grants, PELL, TAP, work study, and federal loans. Family size, relative to income, has helped them qualify for aid, too. We have five kids, with DS2 and DD3 currently in college. I'm concerned about when DS5 is college age, though. At that point we will be considered a family of three, and unless we are FIREd, our income may no longer be in a favorable spot for FA.
Now, I've been trying to figure out if we could fire before DS5 leaves HS, and setting up a Roth pipeline and how it will affect taxes and credits. I was SAHM for 20 years, so I'm behind in retirement savings, but just getting started in a semicareer and still having fun with it, so FIRE for us may be DH retires and I keep working part-time, enough to fund Roths for both of us and be eligible for EITC while DS5 is a dependent, and convert IRAs to Roths. If I put $2k in retirement accounts for each of us, and keep AGI in range, I could convert more tax free using the retirement savers credit, to $35k ish AGI. But, increasing the amount converted to any AGI over $23k ish decreases our EITC. ACA subsidies throw another wrinkle in - depending on family size, we may need higher AGI to qualify. How many people are included in family size at any time depends on whose rules they are. DS2 is 21, and has not been our tax dependent since he started college (earnings and scholarships), but colleges consider him a dependent until 24, and he can stay on our health insurance until 26. We range from a family of four (at home) to a family of six, depending on rules.