I think the limit is 4K, not 2K, for record size. That is PROBABLY because Access uses a 4K buffer size for disk operations. I don't think it has a work area for ordinary records that COULD exceed 4K bytes.
Find limits and specifications for Access 2016 database files and objects, such as the maximum file size or the maximum number of fields in a table.
support.microsoft.com
It says the recordsize is 4000 bytes when Unicode compression is YES - AND it doesn't count OLE or Long Text fields. The reason is that a Long Text or Binary Large Object (BLOB) is stored separately from the main record and the only vestige of the big field/object is a pointer in the main record.
However, there are other issues to be considered. Queries have the same 255 field limit, so these tables' content cannot be managed monolithically by standard table actions and they cannot be managed monlithically by query actions. That would imply that there cannot be a query for sorting the whole table, nor can the whole table be UNIONed or JOINed. EVERYTHING would have to be done piecemeal, which opens the way for all sorts of normalization issues.
The way the U.S. Navy did this was to recognize that their large number of fields could be grouped into topical categories, not all of which applied equally to every sailor. So they grouped the fields and broke up the tables into at least three separate parts, no one of which ever exceeded any of the field-count limits. Then when they needed to correlate the parts, they used JOIN logic in queries to deal with the main table and one secondary table at a time, JOINed across the sailor's military service number. The trick was to assure that no two recordsets, when JOINed this way, also exceeded the 255-field limit.
However, this was done with an ORACLE database and a mainframe front-end database tool other than Access. Oh, they had limits, but they were higher than for Access. The principle might still apply but it would take a LOT of design work to break up the table into pieces-parts.
@jack555 - I mentioned the one case I ever encountered that really could not be normalized down below 255 fields - but like the others in the forum, I find it absolutely unlikely that a table could legitimately have 400 fields that cannot be normalized to a more tractable structure. Normally I would ask to see the database - but you cannot do that because you cannot possibly have built it. Access would have stopped you. Do you have a list of fields that you were proposing?