Nice job on the mods.. I'm sure it will help
Chimney cap, I use one and I recommend anyone to use one. Reason being, some fly ash will accumulate on the chimney surfaces. Rain falling down the chimney will #1 carry the fly ash to the bottom of the chimney and it will build up their (or possibly run down your flue pipe), eventually causing blockage or #2 the combination of water and fly ash creates sulfuric acid that will eat any metal it comes in contact with (for example a metal chimney clean out doorway OR metal chimney liner if either is present). I don't think a cap inhibits draft draw whatsoever unless it becomes clogged with soot, which I haven't seen happen but I suppose is possible if burning bituminous coal.
With coal there is actually less exhaust leaving the chimney than with wood, so the cap should have even less impact on chimney draw using coal. You would need to expel hundreds of cubic feet per minute of exhaust volume for a cap to inhibit any flow. That just isn't gonna happen with a coal fire. A coal fire only expels a few cubic feet (10 -20 cubic feet per minute maybe more, maybe less?) per minute of exhaust volume. That's my take on it
someone correct me if I'm mistaken...