Is there a way to use the D & A (for example) to change presets in my HX Stomp BUT, once I get to that preset, the rest of the buttons (B, C, E, F) reflect the blocks in that preset and therefore control those blocks?
Absolutely, yes. To change Stomp Presets you need your A & D switches to send PC (Program Change) messages. To turn blocks on/off, or change parameter values on any block, you need your B, C, E & F switches to send CC (Control Change) messages. Page 59 & 60 of the Stomp user manual explains it all.
Not familiar with the Stomp, but it seems to reason you could program a separate bank on the MC6 for each Stomp preset. Then on each bank, Presets A and D would send a preset change to the Stomp while telling the MC6 to change banks.