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