The message on a * visa, or a short L visa without a * is: requested to leave China by that visa's expiry date,which will usually be 10 days after the issue date of that visa, or 10 days from the date of an unsuccessful application that was accepted,but not approved for another type of visa.
There's nothing that says you can't re-enter after having had to leave the country.
After leaving the country,imo you've the right to re-enter on at least a 30-day L,as you've already been punished by having had to leave.And note that you were not required to return to your homeland, only to exit China.
I've re-entered after a * visa and a short L, neither new Chinese visa issued by a Chinese visa office in my homeland.
I don't see why you couldn't still do so.But the visa agents will know the situation, they may also know about re-entry with a new passport,which I did recently,because my previous passport had only one blank page left,and after having to accept a 10-day short L backdated to the unsuccessful date of application for an F, which meant I had just 8 days to get out.
But I may have been treated a little better as I have a Chinese wife.However I doubt it. The Beijing Olympics made life difficult for many visa applicants!