Woodworkers: What tool is the most appropriate and affordable for making many large dado cuts?

I’m planning on making a fence from many panels of lattice made up of pressure treated 2×2’s. In order to make the 2×2 lattice, I will need to make many cross-cut dados so the 2×2’s will lock together like Lincoln logs. I found a clip of Bob Villa doing something very similar to what I have in mind. He’s using a pretty fancy radial arm saw with a dado blade.

I don’t have the budget (or room in my house) for large specialty tools like that one, so I’m looking for a more practical alternative. I looked into a table saw (a table saw would be a handy thing to have), but most of the entry-level ones don’t have enough amps to safely power a dado stack and as a result have short arbors that make it impossible to fit. The other option I can think of is getting a router, but it’s going to be tricky to build a jig that can make multiple passes for the same dado.

Any ideas and suggestions for what is the best way (affordably, safely etc) to achieve cross cutting hundreds of 11/16” deep dados, 1 3/8” wide into pressure treated 2×2’s? I would really appreciate any advice you could share. Thanks!