Have you checked the BBD bias’ on a scope? It’s probably just off a little bit. If you lack a scope you can audio probe the outputs and bias them that way.

There is interactivity between the two bias trims (if one BBD is off, the other isn’t going to sound good) so just tweaking them doesn’t tell you much. Build an audio probe and trace through the circuit to find where the distortion occurs.

Taking voltages of everything and posting them is also recommended.

An audio probe may sound like an expensive piece of equipment but it is incredibly simple and cheap to make, all that is required is a guitar lead and a capacitor, see this page https://www.diystompboxes.com/pedals/debug.html Debugging and biasing effectively without some way to check the effects of the trim pots within the circuit will be close to impossible.

It’s unlikely that the BBD’s are the issues themselves and they are fairly pricey if money is an issue.

It could be any number of issues, replacing parts without following debugging procedures isn’t particularly effective and may be a waste of time and money but the electrolytic caps are less likely to be bad than vintage units simply because they’re not as old but they can still go bad.

Posting a full set of voltages for others to look at and audio probing through the circuit to find the source of distortion should help pin point the area of concern.

How strong are the pickups being used as well? BBD’s do have a limited headroom and don’t handle bass frequencies particularly well so with something like EMG’s the behaviour you experience could actually be normal. As the vintage units were not true bypass it was possible to drop the input level below unity gain and have the bypass match the level which isn’t possible on the reissues.