I have also been tempted by this. Many have. But very few actually build a boat with extruded polystyrene as core. Maybe it is because if you consider the total cost of the boat, the cost of the core material in the sandwich is a very minor part. And the risk to gain ratio is not good, because if the core fails, the boat is more or less scrap.
I think that considering how light Harryproas are, they will be cheap enough to build.
I have been doing a lot of calculations to compare the price per square meter with different core and resin choices actually. Considering how much of the cost is epoxy, I think that if you want to save money, it might be cheaper to use a less expensive resin, (and stick to a standard core since. If the core has half the strength as you say, it also needs to be twice as thick, i think. This means that even more resin is consumed in all the holes which has to be drilled through the core to aid the infusion process. The cost of that extra resin (epoxy in the case of polystyrene) is not insignificant.
But even though I have done all the calculations, I keep coming back to the temptation of using it, maybe for the first build. You can get the 20mm thickness with standard density for 2 USD per square meter. Which is to be compared with 20-40 dollars or so for the "real stuff".
One drawback seems to be that the surface usually as some kind of oily surface which the epoxy will not stick well to. So maybe it is better to instead of buying 20mm, buy the thicker (100mm) blocks and slice them to the required thickness with a homemade hot wire cutting machine. But then you have to make that machine. And then you have to drill all those holes. And maybe also cut channels for the resin to flow during infusion. And so on. So it is a lot of work
(when you can buy the proper core which has the channels and holes already made), with little gain, and with an unknown risk of making a really poor sandwich construction. That is my conclusion.
/Björn