Do you have a manual for your loading unit?
If it's an LK - which it does look like, but I'm not sure it is or not - you can find one online. It is a straightforward affair to get at your thermostatic element. Straightforward, but maybe not super easy with your piping. It is located in the bypass inlet. You would close all three of the little built in shut off valves, then unfasten the bypass nut and just loosen the other two. Then rotate the pump, so top comes forward towards you, which would expose the bypass inlet & let you access the element. But, the only time I used those little shut off valves since I started using mine, they all leaked a little bit from around the little square nut thing you use to open & close them with. I have ball valves in the lines further away from the pump, that I will use any other time going forward, and don't plan on touching those little ones ever again (they also turned quite hard, and the little square heads don't give much bite area to turn them with). Plus it was hard to tell which way to try to turn them. So don't force. Looks like you don't have much in the way of in line ball valves to isolate components with, in case water starts spurting - so that may or may not be something you want to tackle during the heating season. If you can keep your tanks above 140 on the bottom, you might be OK for the winter. That might take some regular burning though. There also might be a chance, that once you do get things up to the point that return temps are steady above 140, and the element opens up all the way, that whatever is blocking it from closing might get flushed out through the unit into the boiler, without taking anything apart. I would try that for a while & see what happens - never know. Can you adjust the supply temps to your floor? Via the mixing valve? If so, once you start sending water to the floor, I would start off on the cool side so it doesn't kick the stuffing out of your tank temps. Then bring them up a bit over a couple or few days. I suspect that will be a huge load to your system, as 1" of foam is kind of on the light side for insulation underneath.
Some things to think about for next year. Can't see from the pics, but if it isn't a downhill run from the boiler outlet tapping, to the loading unit bypass T, there is a potential high place there before that line goes down to the cast rad to trap air. So might be a good place for an airvent. Or might be OK, since can't tell from the pics, and sounds like things are flowing. Also on the rad, making use of the water going by to get heat in the room isn't a bad idea, but I would consider plumbing the return water through it rather than supply water. But I was also expecting to see more than a 5° drop through it. Is there any kind of filter or strainer on the system? I used a Wye strainer, in my return line, upstream from the loading unit. Wye strainers are likely the least capable filter you can get, but it should get the biggies that might stop an element from closing. And I would invest in some ball valves so you can isolate things without having to worry about draining a whole bunch of water.