can the DG1022 make that waveform very easily. I found that unit for around $500 which is pretty much what I was looking to spend.
Problem with the DG1022 is the PC software. You don't want to type in up to 4000 values, each requiring 5 or maybe 10 key presses, for an arb waveform on the front panel. So the PC software is important. And in my experience it is absolute junk. Others claim it is wonderful. And service from Rigol is non-existent, especially if you buy from the grey market.
The also mentioned Hantke DDS 3x25 also comes with awful software, but there is some third-party PC software which is supposed to be good. And service from Hantek is non-existent.
By the way, your specification is incomplete. E.g. output amplitude is missing. The DDS 3x25 is a weakling when it comes to this. And most super-cheap generators, not the least DIY generators, have similar issues. The developers stopped after the digital part, and gave up when it came to a good analog output stage.