Before you tear everything apart, I'd start by using the P of E (process of elimination) ..... one item at a time.
You may have one of two problems;
One..... the key switch itself whereby it is not making Ignition circuit continuity while in the "start" mode. This may explain why the engine will fire only when the key switch returns to "run" mode.
(IMO, it's never a bad idea to replace an old key switch)
Two.... the Start By-Pass circuit relay!
There will be a small five pin relay on the engine that momentarily supplies a full 12 v to the ignition coil during cranking only. Essentially this by-passes the Ballast Resistor during cranking due to the heavy amp load of the starter motor. If this circuit or relay is bad, it too would explain why the engine fires only when the key switch returns to "run" position.
(IOW, during cranking, the voltage to the coil may not be enough to allow for a good spark!)
This image and the Volvo Penta schematic both show the AQ151 using this relay.
It may be located at/near where the black arrow points.
It's shown below as SEQ #38
Check to see what the voltage is at the + side of the coil during "Igniton ON".
In normal "run" mode, the voltage will be reduced.
Check to see what the voltage is during cranking.
During cranking only, the voltage will be close to a full 12 v.
Check this relay, and see if all wires are connected correctly.
When done correctly, the P of E will never let us down! 
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