Long distance required between photodetector and TIA
1 - Noise pickup on the leads is not what you need to worry about. If nothing else, you can put your detector in a shielded enclosure, with filtered power in and a hole just large enough for the IR to illuminate the array.
2 - What you do need to worry about is (as Kevin White commented) the effects of those long traces on the input capacitance of the op amp. Unless you properly compensate with a capacitor across the feedback resistor of your TIA, the circuit will oscillate. Fortunately, your frequency requirements (&lt;100 kHz) are fairly modest, and I'd guess you should be able to get a decent signal amplitude.
3 - You may need to go to a multi-stage amplifier chain, with the maximum gain of the TIA (set by the feedback resistor) being limited by the feedback capacitor. Subsequent amplifiers will degrade the SNR of the signal slightly, but that's unavoidable.
4 - 40 LTC6268s in close proximity is, frankly, a disaster waiting to happen unless you are very careful about ground paths and power decoupling. Whenever you have multiple high-frequency op amps you need to take care that a signal on one does not affect a neighbor due to coupling through the power supply lines. And, at 100 MHz open-loop bandwidth, the LTC 6268 is a good example of a high-frequency op amp. You might be well-advised to go with an op amp with a lower bandwidth, such as 10 MHz.
5 - Given the fact that your photodiode array has a reverse bias limit of 6 volts, the example TIA shown on page 1 of the 6282 data sheet is an excellent place to start, keeping in mind the need for an overt feedback cap. 1 uA / 20k will give a signal of 20 mV, and you may (or may not) be able to get away with a larger feedback resistor. You can then boost the signal with a subsequent op amp. Since your bandwidth isn't too great, you should be able to provide enough gain without too much extra noise being introduced.