I think we are all talking about slightly different issues at the same time. I believe the Gary can build an inexpensive and reliable DHW system and size it to provide as much water in the winter or summer as the OP requires. I believe that pdf27 can size a solar thermal system to provide DHW and most space heating, for any coordinates on the planet. I can see that for winter input, a vertical flush mount panel on a wall makes a lot of sense, thanks.
But my kickoff question goes unanswered.....how big a system does semipro need to save how much money? If he was burning oil for DHW (as I am), he would be spending ~$1200+/yr to heat water and $1k solar DIY system like Gary's would look great....clearly <2 years even if the backup operating costs are included. BUt that is the wrong calculation....For <<$1k DIY our oil burner could put in a conventional elec tank, and run an annual cost of say, $600. If the elec backup on the solar HW system is 30% of the total (many are worse), then the operating cost of the solar is $200/yr. Now we're only saving $400/yr. Optimally, that system would be highly tilted, on the roof, to get lot of output in the summer, and wouldn't need to be that large to get the $400 savings.
But Semipro has a HP DHW system. When I pushed my numbers, I figured that during a 3 mo heating season, I would run COP=1, and the rest of the time, I would run COP=3. in 1/4 of the year, I am conv elec, $600/4=$150. For the other 9 mo, 3x longer but 1/3rd the elec consumption, another $150 or a total of $300/yr. So now the question....how much does a given system save? A modest sized, highly tilted system might provide 85% of the 9 mo usage and 50% of the winter usage (70% overall as above), and would save, if I calculate it, $200, and the HP would still use $100/yr of elec for backup. By doubling the size and vertically mounting it, etc, Semi could save a little bit more ($50/yr?), for a lot more effort and visual impact, etc, so let's skip that.
So now Gary's $1k DIY system has a 5 yr payback (at zero cost of labor), and my $6k after rebate commercial system has a 30 yr payback (relative to a HPWH), or an apparent 6 yr payback versus staying with oil (not a valid calc IMO). To me, for a DIY project, a 5 yr payback is getting less attractive, unless it is very easy, or has other benefits, like comfort, resale value, etc.