65 Barracuda daily driver

Check spark plugs for anomalies. If you have a rich/lean cylinder, spark plugs will tattle. Next, check play in the timing chain. If that checks out, put a timing light on and check for timing scatter. Timing jumping around indicates either a bad timing chain (which you can check mechanically) or bad distributor bushings. After that, check cap, rotor, wires, points/condenser dwell (if equipped), and possibly clogged carburetor idle circuit. If all else fails, do a compression test. The old /6's needed the occasional valve adjustment as well. You might want to look at that (especially if you have irregularities in the compression test). Your description opens the doors for many possibilities.

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The new coil may have different dwell requirements. Check the spec sheet.
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The timing chain is new as of last year and it's an 80's hydro-slant, so no valve adjustment. Spark plug wires are the only thing I touched when I replaced the coil, so I'll start there and then timing light and then carb. My guess is that the spark from the old coil was so weak that it affected the timing...