Acros made no M1903 or '03-A3 bolts. There are no bolts marked "88".
There are some bolts marked "CC", which I suppose could look like an "8". But, those were made by Commercial Controls, a WWII spare parts contractor, and are original to no rifle except one that's been overhauled.
Your rifle's bolt should have an "R" beneath the handle. Absence of an "R" likely indicates that the bolt has been replaced. It wouldn't be the first time!
One can only speculate what the "88" in the stock signifies. But, it does not likely have any connection with the bolt.
Hope this helps.
J.B.
p.s.,
Those are two fine rifles you have in your collection. Please share with us some more pictures and serial numbers and barrel dates. Thanks!