I’m a little surprised that there has been little comment on doing FF in erg mode. FF is not so much a workout as a test of what your limits are; having your trainer constrain you to some arbitrary power level defeats that purpose. This is why the description explicitly instructs you to use level mode and why there are numerous visual and auditory reminders to switch to level mode before you hit the first test.
As others have said, which level to choose is a matter of individual choice. But don’t think that you have to use some heroically difficult level to get an accurate test. I’m pretty sure that I have seen no less an authority than Neal Henderson post that he is quite happy to do FF at level one, which also works for me.
The discrepancy between the FTP determined by HM and FF may not be that surprising, given that your rider profile is Sprinter. There are many threads that discuss this and most refer to this article by Coach Mac: 4DP vs Half Monty. HM tends to overestimate FTP for “anaerobically-inclined” rider types such as Attacker and Pursuiter. In my experience, I would add Sprinter to this. My rider type usually comes in as Pursuiter, occasionally as Sprinter, and I have consistently noted that HM gives a 20 - 30W higher FTP and will sometimes also overestimate MAP. A good test of the accuracy of HM numbers is to do Defender or Nine Hammers once you have sufficiently recovered from the test. If you can’t complete those workouts with the new numbers, or can only do so by grinding at low cadence for intervals that should be at high cadence, the FTP is probably too high. I’ve found that splitting the difference between the FF and HM estimates achieves a good balance.
If you are trying to improve your performance on longer climbs (welcome to the club!) @heretic is correct; you are by definition going to be working around FTP and FTP-focused workouts will be helpful. If you haven’t tried it yet, check out RGT as well, where you can test yourself against some iconic climbs such as Cap Formentor, Stelvio or Ventoux. These have the option to dial down the actual resistance if you need to ease into them.
A final comment re climbing is to consider a different cassette. For Shimano systems, cassettes with 30-, 32- and even 34-tooth cogs are available. Long, steep climbs will inherently be at lower cadences. Whatever you can do to up the cadence a bit will shift the load towards aerobic rather than muscular effort; your back will thank you. You may not use the largest cog often, but when you do you will be glad to have it.