That video about the hot water heating of panel collector vs solar panels was quite interesting, thanks for posting that! I was surprised that the solar could produce more power on a price metric, but then, panel prices have come down a LOT. It was also based on a commercially built collector, and I suspect that a DIY version could be made a lot more economical. Especially if you are only trying to achieve temperatures of 70-80F.
To respond the OP, I would say that solar panels ONLY for heat probably is not the optimal solution in terms of cost or collector area. It sounds like you want to drop batteries to save cost (and this is indeed a big savings); but that also suggests that budget is the main criteria. In that case, I think the cheapest way to pump heat into your house would be with black-painted boxes covered in recycled window glass. You would need a little pump, a bunch of black poly pipe, some antifreeze, and maybe a reclaimed radiator to dump the heat inside. You can get cheap little temperature relay controllers that could sense the temperature of the collector to only run the pump when there was heat to recover. I bet you could make a proof-of-concept for a few hundred bucks, and you could scale it up to a real monster of a system for not a whole lot more.
Then again, if you really like the idea of getting some solar panels, here is another option: Get a big array, a tiny battery, and a diversion controller. These controllers maintain the battery voltage during charging not by lowering the solar input, but by ramping up and down an external load. They are a necessity for hydro and wind where you cant simply shut off the incoming power. It doesnt really matter how big the battery bank is, once its full, it will just run the dump load. A controller will run you about 150 bucks, this is one that I have used for this:
https://www.amazon.com/Xantrex-Charge-Controller-Solar-Generators/dp/B000OZ385A
You could just hook it to a big wirewound resistor like this:
https://www.amazon.com/TE1000B1R0J-Wirewound-1000W-%C2%B1440ppm-Bracket/dp/B00W2YQ0QK/ref=sr_1_6?keywords=wirewound+resistor+1000w&qid=1637269098&qsid=136-0514627-8926456&sr=8-6&sres=B07WZ9LTWW%2CB07WPQ2XMC%2CB07WPQ2MXT%2CB00W2YQ0QK%2CB07WYV9P2B%2CB01AA6PGC0%2CB011OZ1378%2CB00MNE0RPO%2CB09KNWMZXQ%2CB09KNV5VLG%2CB09KNTDYQC%2CB072BL2VX1%2CB07SPC8CKK%2CB07WF98SVW%2CB07TLWH927%2CB07D54XMFK
The battery could be a single 12v deep cycle that you can get for about 100 bucks at any battery place.
Since you will hardly use it, the battery would likely last for a very long time, and if the power ever goes out, you could put a 20 dollar inverter on it, and at least have some lights and backup power. Youd be looking at about 300 dollars for the battery, controller and dump load, plus the panels. If you look on craigslist you can sometimes find used panels for a very good price.