Should be doable, but maybe not on that timeframe. If you're really out of shape and haven't been riding much, you'd probably need a couple months of sweetspot and Z2 cardio workouts to get your body ready for that much stress.
But once you have a reasonable base, you should be able to do it. I've trained semi-regularly for the last few years, but never made much progress. Since September I've added about 20 % to my FTP doing mostly 2x20s, long sweetspot and some 5/1 minute intervals.

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See your bike fit. https://bikefitr.appspot.com/

I did something like that. Day 1 5x5 @ 105-110%Day 2 2x20 @95%, Day 3 rest. Repeat until you’re bored out of your mind

I think my max is 15 days.

Always does wonders for 20min power tho

Just a few weeks ago we were talking about 80% of workouts being easy and 20% being hard.

This is completely the opposite.

Are you working out every single day and alternating the two, or every second day and alternating?

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the world's still turning? >>>>>>> the world's still turning

Every day

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Favorite Gear: Dimond | Cadex | Desoto Sport | Hoka One One

This isn’t race specific training. I wouldn’t do this if training for a race. Just off season horseshit. 😁

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Favorite Gear: Dimond | Cadex | Desoto Sport | Hoka One One

Aren't you doing IMCHOO? I'd think this is a good strategy to get mentally fried well before September.

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Dimond Bikes Superfan

My off season horseshit is killing it at the velodrome 4 to 5 days a week.

A bunch of intervals from 15 seconds to 30 minutes.

Are you going to be running and swimming also?

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Let food be thy medicine...

For a athlete that seemingly has been often injured over the past few years and then you self admit "woefully out of shape", it's very much an @synthetic "whatever" approach. But athletes going to do what athletes going to do.

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Brooks Doughtie, M.S.
Exercise Physiology
-USAT Level II

Oft injured was due to accidents and surgeries. Not from overtraining.

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Favorite Gear: Dimond | Cadex | Desoto Sport | Hoka One One

As long as you have something of a base, I think those workouts would get you a decent amount of fitness.

If I could get my act together and get motivated, I would do something similar, though I would stick to two LT workouts and one sweet spot. Vo2 stuff hurts and I don't do that unless there is a good reason. I would be targeting a 30 watt improvement in about 3 months.

However, unless you're underestimating your fitness at 220 watts, a 60 watt bump in 3 months seems a little aggressive. I would assume the first couple of weeks you could go 5 watts every week, but eventually it's going to get harder and bumping the power that frequently might get challenging.

I'm in a similar situation. I had an injury that kept me out of training for more than 2 years, and I'm just getting back to it. My best 60 minute power was 310, so similar numbers. My FTP appears to be about 240. Based on my experience getting back into training the past 6 weeks, I think you're going to have a really hard time maintaining that intensity every day. My top end power is basically still there, but my endurance is way down and my recovery time is longer right now. That's improving, but I really had to ease into it the first couple weeks. When your fitness is this low, it doesn't take much to create fatigue and sore muscles. I've mostly just been doing endurance rides between 140-180 watts and some easy running and I can already tell my FTP is going up without really doing any hard work. I think I've done two real workouts so far. Everything else is easy and the fitness is returning pretty quickly.

I think you can get your FTP up to 280 in 3 months. I don't think that's an unrealistic goal, but I don't think your plan is a good way to try to get there. If your fitness is as low as you say, you could ride easy every day for a couple weeks and make some solid gains.

Maybe your FTP will initially improve by biking less, and swim and running a bit more (do similar or more volume) and drive up your cardio and improve body composition. The other sports can be more time efficient to get fitter faster...and do bike but I think your formula may feel tedious in short order.

I don't know if you injuries prevent you from running, but even if you can jog easy and often, it starts taking care of body composition pretty fast (much faster than cycling)

The reason is irrelevant, your a broken athlete essentially. With your lack of fitness background you have to be even more careful.

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Brooks Doughtie, M.S.
Exercise Physiology
-USAT Level II

I had an FTP ~330 and took about 6 years off. When I came back it was probably in the 210-220ish range, but I had it back to 310 within 3-4 months doing tons of sweetspot and threshold, and back to 330 within 6 months.

Exactly my experience; lots of hard efforts will result in rapid gains of >50%. Even when I initially started riding, FTP maxed out in ~6 months. After I took 10 years off and started up again, it may have been a little quicker.

I'm not suggesting this is an optimal long term strategy, however. I think lots of low-intensity volume with occasional high intensity workouts is better... particularly for people racing longer distances.