120F is scalding hot. Most people who like very hot showers never see exit temps above 110F.
The operating temp of pink foam (=XPS==eXtruded expanded PolyStyrene) ore EPS (bead board) is too low for use in solar collectors of any type, and it breaks down with UV exposure as well. Use polyisocyanurate (often foil faced, eg DOW Thermax), or rock wool batting.
300' of 3/4" PEX is only 7-8 gallons, which isn't much thermal mass- you're very likely to exceed the operating temp of the PEX with that approach, and it won't support a 10 minute shower even at 180F.
To get good heat transfer from your painted foil to your PEX it needs to be wrapped tightly to the tubing with no insulating air-gap. (A tough job, on 300' of PEX.)
A better approach is to submerge a coil of PEX (it doesn't need to be 300', but probably at least 100') in a 30-80 gallon black painted barrel, using the PEX as a heat exchanger rather than the collector & storage. The water in the barrel can be kept at/near atmospheric pressure and should probably be topped off seasonally to replace any evaporation. The up side is that you have more heat stored, the down side is it takes longer to heat up once depleted. By keeping the heat-storage water and potable water separated, there is no chance of long-term water stagnation health issues, which is a signficant improvement over this design. Painting the entire barrel black and using foil-faced iso for insulation you get a fairly good performance boost out of it too, since then the majority of the light/heat is absorbed by the tank, an nearly none is absorbed by the frame or insulation.
If you google [batch hot water heater] you can probably find lots of tips & refinements. Gary Reysa's Build It Solar site is also a good resource for DIY solar water heating info (from the very simple to fairly complex.)