I don't believe the N1 values are minimums; those should represent max values for takeoff, and are temperature and altitude based. I'm looking at a LR35 QRH right now and it states the %N1 numbers are maximum values.
I suspect that what's implied by the inference that they're minimum numbers is the meaning that these values are the gauranteed thrust producers. The only real limitation is the temperature and the upper RPM values. Likewise, published distances won't be valid unless the proceedures published with them are used. A rolling takeoff can't predict where and how fast power application will occur, and accordingly, puts the takeoff numbers out the window.
N1 is an easy to use value, but it also doesn't really describe thrust. It's just a speed, and the condition of the engine and fan, as well as the ambient conditions, really dictate what thrust is being produced. That may be the reason for the data being describe the way you have it; that fan speed is a number that may represent the minimum value to produce rated thrust...though the truth is that the engine may not really be putting that out, anyway.
If I'm setting a preplanned N1 value, I'm of course watching the temps, and may limit the engine before that value is reached, or be tweaking the power back to respect the temps during the roll. It's the engine temp that's limiting, assuming the fuel computer does it's job. If the mechanical goernor/fuel computer is working properly, especially with DEECs, then temp shouldn't be an issue either...but I never make that assumption.
If runway isn't a big issue, then I much prefer to let the airplane roll. I don't like to do rolling takeoffs from the taxiway; I've seen a number of pilots apply power from the first point they start to enter the runway, and that turning moment is very tough on gear. I saw a tire get peeled off the wheel assy on a C-130 that way. I prefer to line up, do a final check, then power up and let it roll. I'll usually hold the brakes for partial power; I prefer to establish a stable power setting and do a crosscheck through all engines, and I think it makes for a smoother power application. It eliminates any low end surges or hesitations if all engines are partially and equally spooled before brake release.
Someone else mentioned not wanting to do full power braked releases. I don't know that excess brake energy is imparted if the wheel isn't in motion, but the lurch as the aircaft comes out of brake release isn't smooth, and it's not good for passengers.
So far as there being problems with the TFE-731...it's one of the best corporate engines out there. I don't know why anyone would be glad to be rid of them.