DustyStyx: Sloopydrew, what type of mouse do you have? Your problem seems to be consistent both with setting Blood up manually and with the GOG installation. You said you had other programs running in DOSBox. I can imagine that any stock USB mouse wouldn't have issues, but it's an outside possibility.
Sloopydrew: I have the GOG version of the game. Any chance you could edit your steps to fit exactly that version of the game, with that configuration? If that's too much to ask, I fully understand. Thank you.
The instructions I provided are what some one would have to go through to manually replicates what GoG offers, from scratch. The main differences being that GoG's default install location is in Program Files rather than the user's profile.
There are a few minor dosboxBlood.conf differences, allocated ram, video mode and using bMouse, but since you disabled bMouse in your configuration, the other settings would not effect your mouse. The other main difference is that Gog renamed the iso and cue files, to something I can't remember just now... but again that would not effect your mouse.
The main purpose of the exercise was for you to gain an understanding of what is going on with the copy you got form GoG, as they are virtually parallel.
We need to determine at what point DOSBox fails on you. Can you launch into Blood? If so, can you move about using the keyboard, and does the mouse have any functionality at all ie, when you move the mouse will the character move back and forth, or turn your view from side to side?