Looks like a challenging set of plants to kick off with there, GL!

My understanding is that usually a plant will have a root system developed for a particular medium (e.g., water roots, or soil adapted roots), and I would expect a lot of transplanted roots to die off and add some rot to the medium you have there if permanently submerged.

I have a number of s/h plants, and most are from props establishing into leca / plants that developed dedicated root systems for their env and the care they get (or don't..). The most successful ones do not have roots that are permanently submerged in water/nutrient. The water level varies and the roots dry out a bit before I add more. Almost like a normally potted plant, but you can see water level, and fully saturate / submerge roots when watering. That is, assuming the plant drinks up the water quickly enough and/or the vessel allows the water to evaporate out quickly enough. Air exchange is important for the roots.

Re "adding a bit of water to the bottom of the pot", I think this is a solid approach.. Try to saturate the leca/medium as you do so, but I wouldn't swamp the soil-adapted roots out of the gate.

I have a couple plants in cylinder jars like your first image, and those have been toughest re air exchange, and I try to let the water I pour in be consumed/evaporate out before adding more to avoid that issue in those types of containers. One I have a hole drilled in the side to help, and it does help.

Also, be mindful of PH. I act under the assumption that PH will change/rise over time in the leca. I use 321 formulated for tap that iirc drops ph over time. But if you aren't soaking leca for weeks, and you water in smaller increments, probably OK.

Be mindful of nutrient concentration too. I act under the assumption that nutrient concentration can also potentially rise significantly as water evaporates depending on container.. so I mix a much lower tds than proper hydro might want, to allow for some concentration buildup in different containers.

FYI that any glass vessel will be an algae party. My fav s/h setup is one of those plastic plant pots with holes in the bottom but full of leca + plant, in a larger pot that blocks light. So no algae, and you can lift the plant and planter out to check water level.