Did you thoroughly clean the main board before you installed the new capacitors (a dishwasher is a good idea to make it really clean).
The original fault taking time to appear makes it look like a heat related fault, when it gets warm, it fails. It could be a dry solder joint or a marginal component somewhere.
The fact you have video out on the VGA port indicates the main board is mostly ok all the way to the CRT video chips on the front left corner, so I'd be first suspecting something on the CRT board first as that image looks like a lack of Horizontal sync.
Luckily, schematics are available, so you can trace it down to a likely group of suspect components.
https://w140.com/tekwiki/images/c/c9/TDS540_Schematics.pdfPage 72 is where I'd start looking. It could maybe just need a tweak of a few trimpots if you are lucky...
I think I have a spare CRT board here so I can take measurements if you need, or sell it to you if you can't fix yours.
