Aye tevi54,
My advice would be to bring forward the small end renewal, it will not be helping you maintain the clearances required for running in a new piston.
Who ever is renovating your small end, either by re-bushing the small end or replacing the con rod, should have the tools, measuring instruments and experience to advise you on the re-fitting of the now damaged piston, rings and the re-honed barrel. When the barrel was re-honed, was it done freehand or in a fixed position? You can make the bore of the barrel not square to the base of the barrel and or face of the crankcase and movement of the conrod and this increases the side thrust on the piston.
Having used fine emery on the piston make sure you wash the piston in hot water with degreaser, rinse thoroughly and the dry, so that no abrasive particles are on the piston afore re-fitting the rings, which also need to be spotless. I would also suggest a new pair of circlips for retaining the gudgeon pin, when rebuilding.
If the piston is of a 'slipper' design then the area of skirt to support the piston may have been reduced when compared with a full skirt piston. Hence the tendency for these pistons to tip in the bore and potentialy have increased wear on the front and rear skirts. Less friction, less weight, higher piston speed, more power, increased wear.

Poke is never free!
Providing the 10.5:1 piston is servicable, go ahead and use it and enjoy the difference that it may make to the engine characteristics. It just might not last as long as that 'standard' piston.
I hope that you soon have the motor running again.
My regards, Bill