The conventional textbook explanations for VX and VY concentrate on jet performance. As you know the thrust and power available curves for prop aircraft conventionally have a different shape, with Thrust vs EAS decreasing from a maximum at zero EAS and with Power available vs TAS increasing initially then falling off.
Because of the different shape of the thrust curve VX on a prop is a low speed, usually less than VMD. Likewise the different shapes of the power available and power required curves show VY to be less than VMD, at or very close to VMP and quite possibly the same as VX, give or take half a knot.
The effect of increasing altitude is to leave the EAS/IAS of VX substantially unchanged because the thrust line moves down and the drag line stays in position. The effect of altitude on the prop power available curve is to move it to the right and down while the power required curve moves right and up. The exact effect of this on the EAS/IAS of VY depends on the exact shape of the power available curve but usually slightly reduces the EAS of VY.
At the absolute ceiling VX and VY must be coincident, because it is impossible to have, for instance, a climb angle without having a rate of climb. The fact that the Islander has them the same at all altitudes indicates a power available curve that is flat around VMP, and that VX and VY both lie so close to VMP as to be co-incident.
Here's one for you, Tinstaafl, as I know you enjoy the theory. I have found an explanation of power available curves on power producing engines from a very respectable source that conflicts with the AP3456 version.
Aircraft Performance by Martin E Eshelby of Cranfield University, (ISBN 0 340 75897 X) Page 59 shows power available constant with increasing EAS and consequently defines VY for a power producing aircraft as being exactly at VMP.
The difference between the two explanations lies in the shape of the power available curve and in the axes of the graphs, the RAF plot power against TAS and Eshelby plots power against EAS. I can't figure out why there is a difference.