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A broken KEY is a symptom that the prop (if the shaft connection is TAPERED) was not PROPERLY honed to fit the shaft ... ... OR if a straight shaft connection - that the prop was installed with insufficient 'interference fit'

An 'interference fit' (press fit) means that the 'bore' of the prop should be 'smaller' than the OD of the shaft - by about 0.001" to 0,002" per inch of shaft diameter. This is standard industrial practice for all shafting involving couplings, gears, and props, etc.
What 'holds' a prop (gear, coupling, etc.) to a shaft is FRICTION between the mating surfaces. In 'good' / standard mechanical design practice a KEY is NEVER used to transmit rotation loads ... the key/keyway is there ONLY as a 'backup'.

If this is a straight shaft connection and your prop 'easily' can be slid off without using a 'gear puller', then there isnt sufficient 'interference fit' or 'press fit'. The usual remedy here is 'new shaft' machined to the proper dimensions; or alternatively, the bore of the prop should be 'welded' and a new proper sized bore machined into the prop. I would NOT agree to have the prop 'over-bored' and a cylindrical 'insert' be 'pressed' into the bore as a remedy, not without WRITTEN GUARANTEE that such a remedy would be effective to X amount of YEARS of service.

If this is a tapered shaft connection, then the surfaces should be 'honed' so that nearly 100% of the mating surfaces are in contact (no gaps of the surfaces) AND the shaft nut should be properly torqued to 'drive' the mating surfaces together to provide the proper FRICTION.
The remedy for a tapered shaft connection is to HONE the surfaces: apply 'bluing' to the mating surfaces, apply 'grinding compound' to the mating surfaces, and while the shaft is held firm the prop is rotated ... until ALL the bluing (and a wee bit of metal) is 'ground' off both mating surfaces.

Summary:
From your description:
If tapered fit, then HONE the mating surfaces
If 'straight fit', then new shaft or new prop.
The max. HP for a 1"Ø shaft is about 30-35HP.
 

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IMO - a (filled) Nylon sleeve will never be able to transmit that HP via a 'friction fit'. If a bore reducer MUST be used, then SS or bronze ... but it MUST be 'honed' for the 'fit' or it too will be vulnerable to 'slip'.

Simple and obvious solution - rebore/reglass/retube the keel, etc. and use the correct and applicable shafting.
 

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Your boat is a renown Bob Perry design.
Id suggest you contact Bob at Robert H Perry Yachts Designers Inc. Home Page and ask him the correct/best way to affect the shaft tube modification (for consulting fee of course).

Id be more concerned about finding the appropriate 'stern tube' (cutless) housing for an increased shaft diameter. Bob would definitely know if a 1-1/4 stern tube/cutless housing from a Tayana-37 or similar design, etc. would have the direct fit up dimensions to your Islander. With your present stern tube / cutless housing change-out to be able to use a 1.25" shaft ... Im thinking that this total 'tube' conversion can begin to become quite expensive.

If this is all too much trouble/expense, Id recommend to begin to seek out the current new prop manufacture's application engineering department to see if they wont sell you an exchange prop with either a custom made 1" tapered bore; ..... or at least, a NON-bored prop hub that can be taken to a 'precision' machine shop to have the proper correct dimensioned tapered bore made (and 'honed' against the current shaft to ensure concentricity and 'in round' of the assembly of the two.) That would eliminate the usage of a complicated weak and vulnerable 'adapter'. If the current new prop manufacturer would agree to a special order, Id also suggest to send them your shaft and let them do the 'concentricity' and honing assembly work of the prop TO the shaft, etc. This would be contingent upon the old shaft being in 'prime' physical shape; otherwise - "Hello Aquamet ........ " Marine Machining & Manufacturing - Home

All it usually takes is lots of boat-money !!!!!!!
 
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