It’s here that I’ll report how this situation might be handled as Anglicans might handle it (though from a slightly different set of presenting circumstances).
First, Anglicans (rightly or wrongly - a different discussion) “fence” the table differently than other Christian communions. Our communion is not “open” in the sense that anyone is entitled to participate. Rather, all members of the church are invited to partake IF they are baptized with a Trinitarian formula (i.e. "in the name of the Father, and of the Son, and of the Holy Ghost), using water (any mode, but only water - not milk, not iced tea, etc.), and if they are not under discipline in a congregation where they were previously members. This policy may be criticized, but that’s a different discussion.
Now, a common question for the Anglican priest is this: has the prospective member (or participant in the Eucharist) ever been licitly baptized? For some, this is impossible to know. If he were baptized as an infant, he would not remember the event, of course; and, he may also not know or remember a report of such a baptism.
Meanwhile, in Western non-Baptist understanding of baptism, the rite only occurs once. It’s not an event which should (or even ccould) be repeated, though the ritual motions might be repeated, obviously.
What to do if someone presents himself for membership in an Anglican parish or to receive communion in an Anglican Eucharist if he does not know if he has been baptized licitly or not?
In an Anglican setting, the parish priest conditionally baptizes such a person. In all its details, a conditional baptism rite is identical to a conventional baptism except in one detail, namely the formula which the priest speaks prior to the application of water (by whatever mode).
“I baptize thee [name of person being baptized ] in the name of the Father, and of the Son, and of the Holy Ghost,”
the priest says
“If thou art not already baptized, I baptize thee [name of person being baptized ] in the name of the Father, and of Son, and of the Holy Ghost.”
In a conditional baptism as described above, the words spoken are the same as in an ordinary baptism. However, in a conditional baptism, all persons present understand that the rite might not be a an actual baptism because such an event has already occurred previously. Thus, no previous, licit. but unknown prior baptism is repudiated by anyone participating in the conditional rite.
If something similar were practiced by (actual or virtual) Baptist church officers, they relieve the person who was baptized as an infant from repudiating what his conscience acknowledges as a prior, valid baptism. Of course, if the most recent rite requires the person being baptized to make a public, express repudiation of a prior rite, then a conditional baptism as described will not solve the problem.
Moreover, in a conditional baptism, the Baptist church officer is relieved from acknowledging as valid what he deems to be an invalid baptism. All present leave it up to our Lord to judge if, when, and how a licit baptism was performed, while all involved agree that a licit baptism was (or is being) performed.