Start with the basics. Assuming it has solid lifters, check the valve lash. If the valve lash is too tight it can cause problems such as this once the motor warms up. If that's not it, rig up a fuel pressure gauge that you can observe while driving and see what the fuel pressure situation is when the problem occurs.
If the fuel pressure is OK, I would bypass the ignition switch to make sure that you don't have an intermittent open circuit there. I just drove my Hemi GTX 2600+ miles on Drag Week, and it does not have Holly's and I had no issues. You don't need Hollies, you need to find the problem.
Good luck