It can be done with a little control circuit but then the cost implications outway actually rectifying the original problem and since you are not set on sorting out the original issue then creating more work at a bigger cost is not viable.
One last kick at the can. I realized that my previous reply wouldn't work as intended. But if I were to power the single-pole switch by pigtailing off the red wire in Box 2, then I'd have direct power as long as the 3-way switch in Box 1 was in the "red" position. Since it's only a couple of steps away and we'll mostly just be using the LED fixture, this will be a good compromise.
 
So what you are saying is you're going to have to stop using one of the switches altogether (box1) to ensure power is retained on the red strapper which you can then tap off the fluorescent switch supply in box 2, this will cure your dilemma with having to have the LED's on at the same time which you won't need to now but you have basically converted it into a 1way system, the only drawback is if you accidently use the other switch you have to mess about to set it in the correct position to use the fluorescent...
Basically you have shifted the problem from box 2 to box 1 as you still require another switch to be in a certain position to allow your fluorescent to operate.
If this is acceptable to you then fine but it is crazy logic in my mind, you defeated the whole point of having 2 switch points to turn on the LED's from.

I think that all this time and effort trying to resolve this could have been better spent actually addressing the original wiring issue, is there absolutely no access to the wires in say a loft space or by lifting some boards to correct the original mistake?
 
If for some reason I have to open walls in the future, then I'll run the necessary cable to correct the two switch points. But pulling cable through the walls and ceiling is not something I'm up for. Floors are all concrete - no floor boards.
Maybe 'crazy logic' for someone who makes their living as an electrician, but for me it's just the easiest acceptable solution/compromise without making this into a project. I have plenty of other higher priority projects I'd rather spend my time on. Seeing as I was not an electrician, but nevertheless wired my entire house (except for the 'consumer unit') when I built 19 years ago and this is the only electrical issue I've had to deal with, I'd say I did alright. It's a minor inconvenience really, since we prefer to use the LED task lighting, would only use the fluorescent infrequently, and the switches are just a few feet apart anyway.

Cheers
 

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3-Way Dimmer Dilemma
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Lighting Forum
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Yukoner777,
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