I sense your frustration in not getting the performance that you expected. Here is some math that might help you start to understand and evaluate your system. If as you say your boiler output is maximum 250,000 btus, and if the Side A differential is 10 as you show in your specs, then you need to be moving 50 gpm (250,000 / 10 / 500) through Side A; and to move that same volume of btus through Side B to get a 10F differential (180 / 190), you also need to move 50 gpm through Side B. Obviously, if your boiler output is less than 250,000, the gpm needed to maintain a 10F differential goes down.
If the math is applied to your 750 gal of storage, and your goal is to raise storage from 140 to 180, for example, the btus needed to do this, by coincidence, is only 250,000 (8.34 x 40 x 750). In an efficient wood gasification boiler, the amount of seasoned wood to deliver these btus is just 49 lbs with an efficiency of 85% (250,000 / 6,040 / 0.85). 49 lbs is about 6 nice oak splits at 8 lbs/split.
As Bob stated above, 1" piping, if that's what you have, pretty much limits you to maximum 12 gpm flow rates, Sides A and B. What I don't see in your posts is the calculated pump head at any flow rates on both sides of the hx. With a good pump head estimate at various flow rates on each side of the hx, it's possible to make some real progress in sizing an hx.
Let's assume all of your piping on both sides of the hx is 1" pex, straight only, no L's, curves, valves, etc. How may feet of pex do you have on each side of the hx? Look at the charts for 1" pex and determine the pump head ( = psi drop x 2.3). Calculate pump head for 12 gpm and various other flow rates you think are realistic. Report back the feet of pex and the calculated pump head and, at least for me, I will have some info that can start the path to sizing an hx for your system. And also provide a realistic btuh boiler output you want to move from your boiler to storage. If you're thinking 250,000 through 1" pex, that's not possible in my opinion.