My Greenish Power Project and Updating a Few Grid Cords

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I presume 20 kWh per day, not a max of 20 kW.
That, imo, will never be done with dinky solar panels.

I have 20 panels of 360 W, so 7.2 kW. Half facing East, half facing West on a rather low slope roof. Some trees affect generation after 3 pm in summers.

I produce, on average 17 kWh per day. 35 on high days, and zero on snow days. Total yearly production divided by 365 is 17 kWh .

You are farther north, have more cloudy days, but can orient your panels better.
I think you'd need at least 8kW to get 20 kWh on average (i.e. more in summer and much less in winter).
That's 40 200 W panels...!
yes, per day. Dang that's a lot of panels! I'm thinking we use too much electricity!

I do have fairly clear sun on sunny days with minimal shading. I don't want to cover my house with solar panels either. Well, I guess we will see where this goes!

Would you start with a big solar generator and build on it or home brew your own DIY setup? I'm really crunched for space. I'm not sure I can squeeze a DIY setup into my utility room or not. It's pretty tight in there already.
 
It depends on the goal.
If you want to end with whole home off grid,.do it right from the start. Finagling small diy parts is going to be orders of magnitude more expensive than biting the bullet for one big system.

But I think you should not do that given your time horizon.
Get a few panels and (<5) batteries for the essentials, and call it a day.
You wont make your money back anyhow with such small parts. But it gives peace of mind.akd that's worth something.

So peace of mind by having your essentials taken care off piecewise, and then spend any other money reducing power usage and increasing insulation and air sealing.