First, none of the start / ignition wiring even goes to the fuse panel
You say you would like to keep turn and lights, etc, this sounds like you are going to drive it.
A few photos might help, you have lots of options depending on your skill, budget, purpose of the build, condition of the old harness, your goals, I mean "it's complicated."
Some options:
You can buy aftermarket fuse panels, or even salvage one out of a later model car
You can pull out the harness and rework it, as completely as you desire, or at least repair it
You can buy "original style" rep harnesses
You can buy generic "budget" so called "11 circuit" or "12 circuit" etc etc "hot rod" harnesses
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Now..........going to a push button might actually be more difficult than you might think...........
This is because the IGNITION SWITCH in a Mopar handles the coil resistor bypass function. This is almost unique in American cars. In GM / Ford the bypass function is done in the starter solenoid
Look at your diagram...........the ignition switch is NOT that hard, what you have:
1.....Main battery feed coming IN to the switch. This is NOT fused other than the fuse link in the engine bay, and comes off the ammeter circuit black wire, the "welded splice."
2....Accessory feed going TO the fuse panel from the IGN switch. This is hot in either ACC or "run." The fuse panel has TWO busses, one hot at all times, the other this ACC feed, and the fuses feed "out" from there
3..."Ignition run" or IGN1. This is hot ONLY in the run position, feeds the instrument cluster, warning lamps, and out through the bulkhead connector, where it branches off and feeds the ignition system (run), the blue alternator field wire, the voltage regulator IGN terminial, some smog doo dads, the electric choke if used
4...."Bypass" or IGN2, usually brown. THIS IS HOT ONLY in start and ONLY has one purpose......it bypasses the coil resistor, and provides ignition power during "crank."
5..."Start" usually yellow. This feeds out through the bulkhead connector to the starter relay, to one of the "flag" "push on" terminals and activates the starter relay if..........
A....the neutral safety switch (automatic)has............ or
B....the clutch safety switch has...........
.........grounded the remaining flag / push on relay terminal