There is a solution. It is to find a reasonable theory of noninferential justification for basic beliefs, and to describe what sense of basicality is more probable (DB or EB). So far, no one has taken up this task specifically, except to say noninferential justification is incorrigible or self-evident, when this seems to not be the case and when pressed further for an explanation none was given. Of course that doesn't mean foundationalism is false, just more so that it is seemingly untenable.
Another solution is to just drop any idea of basic beliefs, which I am not sure what the results would be, yet I highly doubt it would be so overwhelming for our epistemological understanding that the result would divert from a sound structure of knowledge. We could go with coherentism, which almost seems like more of a suitable option to me.