Part-1
If the engine cranks in the "crank" position, then obviously the entire brown wire start-circuit is working.
If the engine previously ran in the "run" position prior to the swap, then obviously the entire run-circuit was working.
Therefore, I agree, that the problem must lie in how you spliced those two circuits.
Part-2
On my car splicing the brown and the yellow together, caused similar issues. I installed an aftermarket relay to send battery-power to the CDI box, triggered from both wires, and a DIODE on start side, to prevent feedback to the starter-relay; which solved the problem.
Part-3
But that CDI System (Not MSD) proved to be unreliable so I ditched it and went back to the Orange box/Accell HO coil. Ran that for a while until the Orange Box gave up. About that time I installed a Jacobs, Dash-mounted, dial-back, Ignition-Module, which has been running reliably now, for over 20 years. The big Yellow square top Coil, is amazing. It's been to 7200 probably thousands of times.
BTW
In my experience, I have found reluctor gaps from Zero to .030, on good running cars; just saying.
Personally, my distributor is over 50 years old, so the top bushing is a lil worn, and so, I set the reluctor gap around .012, which prevents it from touching the pick-up. She still goes to 7200. and she still idles down to 550 in gear, pulling herself, at 5* of Idle-Timing, achieving a sub-4 mph roadspeed. (3.09 low/3.55 gears)..