There's a difference between wanting the capacity to spend 100K in retirement, and actually spending 100K, without fail, every single year of retirement.
Are you really expecting to spend 100K, every single year, even in the event of a major market crash? Really?
Because that's what you would have to do in order to justify a sub-4% withdrawal rate.
If you really can't afford to save to your completely arbitrary "fat FIRE" target, then it's a nonsense target.
As for defining fat-FIRE vs FIRE vs leanFIRE vs barista-FIRE vs coast-FIRE, those are all basically personally defined according to the particulars of the people involved.
It's especially hard to define coast-FIRE/barista-FIRE because that depends entirely on how long the person wants to continue working part time.
DH and I can make solid incomes working very casually, so 10+ years of just letting our 'stache grow is highly probable. So whatever number we aim for, it will likely end up nearly double.
Though that's only because we love our work and our spending is much lower than 100K. It's also easy to love work when you only have to do it 1-4 days a month in order to cover your spend.
Pete has spelled this out pretty clearly, the greatest financial power you have is in lowering your spending. It gives you maximum flexibility on all fronts.
So if I were you and my desired arbitrary target was unrealistic, I would examine all of the factors involved and adjust accordingly
1: current spend- is it too high? Could you be saving more to reach your goal?
2: WR- 3% is absolutely nuts, especially at those higher spending rates where budgets can be drastically cut in bad market conditions.
I personally have a hard time believing that the kind of people who are conservative enough to plan for sub-4% WR are also the kind of people who won't cut back their spending during a crash...which makes the low WR moot, but whatevs...
3: planned future spend- again, are you *actually* wanting to spend 100K every single year??? Why??? If not, then see #2 about sub-4% WR and reexamine what you think actual risk is.
4: do you have any work you see yourself doing once you leave full time employment...this opens a HUGE mathematical can of worms, in a good way, but it definitely complicated things and gives you many more options.
Just because you asked for it, I'll give you my numbers
-WR: not really all that relevant as there's a FED pension, a rental, and a lot of flexibility in our spending. So let's use a basic 4% and consider that extremely conservative for our case
-leanFIRE: 1M condo not paid off, this would readily fund our lifestyle, but in a given year, things could be tight with a large unexpected expenses. That's as lean as we would ever possibly go, I would much rather work more than have less than this amount of security, so it's a bit high for a true leanFIRE.
-FIRE: 1.5-2M (mortgage is irrelevant at this point), if I had to stop working or decided to stop working, I would be rather comfortable rolling with large unexpected expenses and could readily adjust spending if needed while not compromising on happiness.
-fatFIRE: 2-3M at this level I would have to inflate lifestyle to not end up with a giant pile of cash when I die. These lifestyle inflations wouldn't actually change my quality of life, they would just increase the fanciness of aspects of the life I already have while failing to improve it in any kind of appreciable way.
coastFIRE: there isn't really a number for this, besides, I already only work part time. It's really a spectrum involving any level of income that lowers your WR, which can range from covering your entire annual spend to just reducing your WR in retirement.
Sustaining some level of income provides A LOT of flexibility to any plan, especially with a low spend.
barista-FIRE: basically coastFIRE, but doing low(er) skill/low(er) pay work instead of cutting back on professional level work. I wouldn't do this, but DH might take up personal training if he ever stops his professional work.
I have no idea if my personal numbers are of any use to you though.