Thanks for an interesting question — let’s break it down using your numbers.
If we assume your FTP represents your maximal sustainable aerobic work rate (what I refer to as “Critical Power”, or CP), then CP = 250 watts.
Now, if you can only hold 200 watts after a 1-minute all-out effort at 350 watts — which you say fully depletes your anaerobic capacity — that might suggest your CP (FTP) estimate is a bit too high. But that’s a side point.
Let’s calculate your "anaerobic work capacity’, W′ [pronounced “W-Prime”]
W′ = (P - CP) × t = (350 - 250) × 60 = 6,000 joules = 6 kJ
Respectfully, 6 kJ is quite low — typical W′ values for adult males are often in the range of 15–20 kJ, and slightly lower for females. But let’s continue with your numbers.
You didn’t mention the length of the climb, so let’s assume it’s 10 minutes. Is a 1-minute maximal effort at the start optimal? Probably not — as you noted, you’d likely need to back off for a few minutes to recover.
Instead, imagine you spread your W′ evenly across the whole climb. You could ride at 260 watts (10 watts above CP) for the full 10 minutes — that’s a smoother and more sustainable effort.
You’re really asking how to train for that moment when your friend (enemy) attacks, and you need to respond.
So, let’s say you do some high-intensity intervals and DOUBLE your W′ to 12 kJ. That would give you the capacity for:
350 watts for 2 minutes , or
270 watts for 10 minutes (meaning you’d finish the climb in around 9:30 — a solid improvement).
However, rather than trying to double your W′ (which is difficult), it may be more productive to increase your CP — which is generally easier to improve with training.
A 10% increase in CP would take you to 275 watts. With this higher baseline, you could:
Ride the climb faster at steady state,
And still have W′ to use on top for a final effort or response to an attack.
Physiology determines performance. Improving your physiology — whether that’s through raising CP, increasing W′, or both — improves your performance.