Meis only says .....
that the Serial Books give NO DATES in the period from 1894 to 1897. He does NOT say, the books are faulty in that period. And he couldn't say that, simply because of the fact that there was nothing to crosscheck against.
In fact Meis as well as Toelke/King are based on the Serial Books ONLY and so both books inevitably convey the mistakes of the Serial Books to nowadays collectors.
By now the Movement Control Books have been found and allow to check these against the Serial Books. And from time to time a series says it is a series of calibre x, while a closer look in the Movement Control Books reveals, out of three hundred there were 288 calibre x, but as well 12 calibre y. But this is not the rule, but an exemption. The bigger problem are typos.
Toelke/King is a very careful written book, but it couldn't provide more data than known in 1986 and it doesn't claim for impeccability.
And what you pointed out is not a specific problem of the period from 1894 to 1897. When checking movement Nos. regularly against the Toelke/King you will find that there are mistakes over the whole period covered by the book. Most are typos as I know from Mr. King, some are caused by mistakes in the Serial Books. A rough estimate is, that in about 5 of 1,000 checks you will find Toelke/King to be faulty.
Regards
Th. Koenig