To answer your question about the transparent shield you should endeavor to locate the source of the roomy sound.
How many drum mics are we talking about? Are the drum mics set up close to the drums or are they distance mics? Do you have someone who is familiar with mixing drums working on the mix?
Close mic-ing drums will get you and up-close sound.
Is it possible that the roomy sound you are getting is from bleed into other mics like a guiitar amp's mic or a pulpit's mic?
If you figure out where the roomy sound is coming from you can go to the next step and decide if using some sort of acoustic screen will be helpful.
best regards,
mike