No need for energy minimization. Start the equilibrating molecular dynamics simulation at very low temperature, with very short time-step, and with strong coupling to the bath.

Mary Pitman I was trying to edit my first answer and accidentally deleted it. So, my question was, "Are you asking if you can, for instance, minimize different domains of your protein, or perhaps, minimize the water and then the protein/membrane, but in different steps? And then stitch those minimized structures back together?

If that's what you're asking, it's an interesting question. I'm not going to say it's impossible but I'm not sure it would work practically. First, I think it'd be difficult to find a way to accurately split up your system in a way that is true to your protein's allosteric network, or that captures the shell of waters interacting with your protein/membrane. Second, I think it could be troublesome to put back together. I tend to think of the minimization's primary objective as slightly adjusting atoms that are too close together, or otherwise in an energetically unfavorable conformation, because if we didn't adjust them, they would accelerate far too quickly during equilibration and cause the system to "blow up." So, when stitching these systems back together, I imagine it would be difficult to ensure that there aren't any weird atom overlaps or unfavorable conformations. Stitching them back together may increase the odds of your system blowing up.

To add on though, Martin Klvana brings up a good point. You could drop the temperature and decrease the time step and just do a longer equilibration to relax your crystal structure out of any energetically unfavorable conformations. This will lower the chances of your system blowing up because the energy of the system is so much lower. That said, I don't know that it would really solve your problem of minimization taking too long on a busy HPC. I imagine equilibrating at a low temperature with a short timestep would take as long as minimization, if not longer.

I think your best option is to do what Nebojša Zec