my swipe about grass was really one of those 'permaculture smug bastards' sorts of thing about the grass itself - as in, don't grow a crop just for walking on and looking at, but rather either let it go wild or actually farm it. I realize not everyone can or wants to go 'full rebel' in landscaping. I totally am on board with figuring out how to save water and not buy it.
Actually, one thing about 'not grass' would be that a natural landscape would probably be a better buffer for storm water and in addition, not need watering in the dry times. So, rethinking your project and doing more swales and trenches and landscaping might be the lowest-impact, best long term solution. still, that's just more smug permie talk.
about burying the tank: I think you're right, it's because it could collapse if it was empty on the inside. and yes, basically building a basement around the tank (with cinder blocks, or treated wood, or poured concrete or something) would work. but that's a lot of work just to not look at a tank. you might just look around for a different sort of tank that CAN be buried. a new septic tank (that is, never used, so it's clean) with a few plumbing alterations could be tossed in a dirt hole.
now, about saving water:
So, if I'm understanding, you're planning on having all the water from the house roof AND the french drains go to a 50 gallon barrel downhill, and then have a pump in that barrel that moves 1500 of it uphill to a tank? Even if it's just one of those sources of water, you'd better do the math on how much water will be hitting that garbage can at one time.
example: my house roof has about 2000sf of surface. that means every inch of rain, I get 1200 GALLONS through the downspouts. Like you're experiencing (and we all will, as climate change keeps messing us up) I get 7 and 8 inches of rain in 24 hours.
That means, conservatively, I get .33" an hour of rain, or 400 gallons an hour down the spout. if your house is anything like the size of my small house, your pump is going to have to work REALLY FAST and REALLY hard to keep that garbage can from overflowing. AND, if you have that strong of a pump, and you have that much power during these big storms, in a little over 3 hours, your HDPE tank is going to be full. then you'll have to turn that pump off.
Which to me sounds like you're going to have something of a pond down at this point on your property anyway.
Maybe I'm looking at your situation with jealousy, as I've been dreaming of ponds up on my place, but my slope and access doesn't allow me the space or tractor access for a real pond.... but I'm still thinking this is my best advice. Digging a big hole in a low spot and then managing it for good ecology (meaning - getting fish and things in there to keep the skeeters down) and being able to drop a pump line into it for filling up a 1500 tank multiple times throughout the summer seems like a wonderful bonus, rather than a complicated piping-and-pump-back artificial system.