First, for a very simple analysis, see this:
https://www.mrmoneymustache.com/2012/01/13/the-shockingly-simple-math-behind-early-retirement/If you want to retire in 7 years, that means a 75% savings rate. You already have a couple of years' expenses saved, so you wouldn't need to go quite that high, but it would still require a very dramatic change in lifestyle. So I agree that that is unlikely. OTOH, you're currently spending all of the take-home income from your job and then some, so you can change your timeline to FIRE quite dramatically with more minor lifestyle changes.
You're already in a good spot with the student loan almost gone. But your top priority at this point should be to shove as much as you can into tax-deferred retirement accounts, because that is where you will get the biggest bang for your buck long-term. I mean, it's great to have a paid-off house, but you also need invested assets generating cash to cover all of those other expenses.* And the power of compounding says that dollar that you put away today has far and away the most significant impact on the amount of cash you can generate in the future.** In addition, the tax-deferred status of a 401(k) account allows you to put away even more of those dollars for the same hit to your budget.
I do think it would also be a good idea to pay off the mortgage by the time you retire (this is a personal preference, there are many here who would advocate maintaining the leverage permanently). But you don't need that done
now -- you need that done by your target retirement date. So spend the next 5-10 years growing your retirement 'stache, until you reach the point where it will continue to grow on its own to the amount you need by your target FIRE date. At that point, you can shift your extra cash to paying off the mortgage.*** When your mortgage is gone
and your 'stache is at a level to support your now-mortgage-free expenses, boom, FIRE.
*Do not count your house in your "assets to FIRE with." The 4% rule is based on your invested assets, so unless you're going to sell the house and invest the equity, it doesn't count. Where it does help, though, is giving you a low-cost place to live once the mortgage is paid, which means your overall 'stache can be smaller.
**My standard example is that if you have $100K to invest today, the rule of 72 says that if you average a 7% return, you will have $200K in 10 years, $400K in 20, and $800K in 30. But if you start 10 years later, you end up with only half that amount ($400K) -- same amount invested, same 30 years, because you lose
an entire doubling.
***Illustrated by the above scenario. If you spend the first decade paying off the mortgage (say) instead of investing, you end up with a $400K 'stache that will support an annual spend of $16K. But if you spend the first decade investing and THEN pay off the mortgage while you let that money ride, you end up with an $800K 'stache that will support an annual spend of $32K.****
**** This is obviously way too simplistic and doesn't account for the extra mortgage interest or the fact that no one actually has $100K to invest all at once. It is just an illustration of why the timing can make such a big difference.