One Signal Integrity issue is : no power should flow through the shielding of the scope probe, and in particular no changing current ! This would kill the sensitivity of the probe.

In the #ScoPower I use a short coax cable, and a crocodile clamp. The power supply that goes through the shielding is weak and there is not much influence. The output signal is square and even a tiny jitter is not critical.

If milliamperes have to flow at 1KHz, over a 1m coax, things are radically different. That is why there must be a separate circuit for power, at the BNC base, and the amplifier at the end of the coax. Both circuits are linked with another pair of wires for + and - supplies. The amplifier will just "drop" the voltage with a LDO, and eventually provide some feedback with a sense wire to decrease the voltage of the step-up...

One problem had been identified though : there is no male connector for PCB, only female (AFAIK). However I just found a little nice trick ! A simple BNC "T" connector has 2 male and 1 female sides so I can make a PCB with a female connector, which directly hooks to the scope and reduces the ground current in the coax's shield.

(I gotta draw a picture but I'd rather assemble a prototype instead)

Another issue is that most BNC coax cables are intended for 50 Ohms impedance but the probe scopes have a different impedance... You'll have to sacrifice a probe to connect to the amplifier :-/ Unless you can resurrect an old broken probe and cut its head...