Ok so first off, I assume that the underground piping is some type of three wrap or similar product in a drain tile and I also assume it is a new install. Although a new install I would want to confirm that you aren't losing your heat between the boiler and the house because of ground water getting into that drain tile, that would kill all efficiency. You radiant manifolds should have a temp gauge going into the floor and returning that you can confirm you are getting whatever temp the boiler is at when it leaves.
Next what temp do you have your tempering valve set at to send water into the radiant slab
What is the differential on the boiler? You said 165 high, what temp does the blower kick back on again to bring the water back to 165? The problem with running this really low temp is that the boiler will start to sweat inside the firebox if the return water is below 150. So if you are sending water returning to the boiler below 150 you are causing condensation inside your firebox which is compounding your burning issues as well as causing corrosion. Most of us run at 160 low and 180 or 185 high. The boiler will run more efficiently up in these temps as well.
What do you have for insulation under the slab and for a thermal break between the slab itself and the frost walls?
You should really either forget about burning this punky wood or throw a piece or two at a time with the rest of your quality wood.
I think your major issues are two fold. First major issue is the wood you are burning likely has little heat content or BTUs and without the available BTUs you are not going to be able to rise the water temp.
Second problem I believe is that I think since you aren't sure what a flat plate hx is you are running a totally open system which is a problem for a couple reasons. First reason is that the water quality with junk in it from the owb jacket is going to get into the radiant system and cause sediment build up and corrosion issues, also you can have many issues with purging all the air from the loops in the system is open leading to zones in the floor that are air bound. Also the biggest problem with not keeping the two systems separate is that return water back to the boiler is going to be very cold causing shock to the boiler itself and running issues. You need to really have the systems seperated through a flat plate heat exchanger. This flat plate allows your to build a pressurized system on the radiant floor side and an open system on the owb side. On the radiant side you would have a mixing valve to mix the water down to somewhere around 100 degrees entering the floor and somewhere around 80 when it returns. The flat plate allows you to send 180 degree water from the boiler to the flat plate and then return to the boiler at 160 or somewhere there about(looking for around a 20 degree delta T(delta t = water temp drop) which will keep from shocking your boiler and allow it to run correctly. The picture below while not exactly your situation it is close enough. Your boiler in the diagram doesn;t need a expansion tank on it since it is an open system, it just needs a pump to pump to that flat plate heat exchanger. Now you could set it up like the pic shows with a loop and taking off the loop and sending to each slab or you can just use one pump on each outlet from the boiler(what I would do) and send it to the flat plate. The radiant side is what you want except you would also need a tempering valve added in there as well.
View attachment 192312