Hardware triggering multiple devices from a single source for long distances
Generally, there's a lot of clock distribution ICs from most major silicon manufacturers (TI.com, analog.com, onsemi.com, st.com, maximintegrated.com …) that serve the purpose of exactly this: distributing clocks.

However, at your distances and your frequencies, the problem really isn't what these were built for.

Note that your schematic is a bit ambiguous: when driving long lines, you'd definitely want a defined termination impedance, i.e. effectively, some resistance to sink power into.

Ideally, I'd recommend a differential line driver (for example, the ones specified for RS485) for each of the lines. There's multi-port devices that you can use to implement this.

Cost-wise, a simple multi-channel opamp with some drive strength can be used in a voltage follower + inverter way to generate your differential signaling. That would only need the opamp (and maybe a decoupling capacitor on the power supply), and termination resistances, and no further components, and would be super cheap.

With the multi-core transformers as found in every Ethernet devices (super cheap!) you could implement the same balanced (==differential) signalling with only one opamp channel per trigger, with the added advantage (or disadvantage, depends!) of allowing separation of potentials.

Generally, 1 ms is pretty doable with standard computing and wired networking hardware – a single board computer at each end (e.g. raspberry pis), and a network switch (or, hub, really), as well as one line of netcat command line could implement the same functionality, and if you need logic at every end, anyway, that'd allow you to reduce your overall complexity and potentially cost. 200m of copper twisted pair fast ethernet cabling isn't 100% legal by the standard, I think, but it usually works reliably. Generally, using full computers to do this is total overkill – I just wanted to mention this option in case it solves problems further down the line.