The solution is: don't use bridges or anything with a delay, use mass doors or hatch covers for output.
I was once working on a "dwarven time machine" project as I called it. There was 4x7 screen made of 28 doors acting a pixels. It was meant to show successive digits 0->1->2->...->9 then repeat.
There was a counter made of 10 pumps in a circle that pumped one tile of water around, with 10 pressure plates between them, each showing another digit. There was a big cistern with pressurized water above, and a small cistern below, with towers of pumps draining the water back into the upper cistern. Cisterns were connected with 28 channels, one for each 'pixel'. Every channel had 10 'entrances' covered by 10 floodgates each opened with one of the digit pressure plates. Or not opened if that specific pixel wasn't active for that specific digit. So there was 280 floodgates total at the bottom of the upper cistern. Each of the 28 channels had one exit with a pressure plate in it, connected to one of the pixels. So if any of 10 floodgates allowed water flow in that channel, the corresponing pixel will show.
Hmm... At least that was the idea. I had everything planned how it should look like, but got bored with the project at quite an early stage. I may try it again after the next release, so at least I won't lose it to broken save compatibility, so future dwarven engineers could admire it. If only it is going to work, which i am not really sure about.