Had a little time to look up waffenamts in the Republican era, though I have no formal trends of such acceptance patterns outside of Simson and Zeithain production trends work. The only certain connection is Zeithain in 1927, a good range of the production have RR WaA16 (only in 1927 though), but I do not have any example that is original bolt matching... though I would say such a serial in the 4500 range would be far beyond what trends suggest as normal ranges for that year at Zeithain, though we know very little about this HZa and their production 1924-1928(*).
We do know that they (Zn) also reworked G98's during this period, though rarely, there are a couple of Imperial rifles that carry the Zn atop the receiver, but retain some of it their original parts (and original serial), - though carry Zeithain waffenamts under the original Imperial acceptance.
I should say, although this doesn't necessarily demand corresponding adherence to Simson patterns (Simson being a private concern, operating under contract making new rifles and pistols, necessarily would have a more formal pattern), Simson "generally" used E/6 for early bolts although 1925-1927 they were inspected by E/14 also, but so far only E/6 bolts are known (so few exist that we should hesitate in our certainties - but "it seems" while RR may carry other waffenamt inspectors, in this time frame bolts, barrels and components carry the primary inspector), though in later production E/43, E/46, E/76 & E/81 bolts and components are seen.
I checked WuK also, no luck on E/16, almost all are E/61 early and E/46 for most of production, though HZa Su/25 is seen on a number of bayonets, I assume passing through Spandau at some point.. they are a queer lot, very diverse, lots of RM use which may account for this diversity.
Lastly, I want to say Rheinmetall has an association with E/16, though I didn't seem able to confirm it in the limited time available, but this would hardly make a legitimate link to a rifle bolt. If I get the time I will see if I can find out my observations on Rheinmetall production, but there was an early (low, might be E/14) waffenamt used on their equipment, but may not be E/16.
*** in short, if you have a E/WaA16 bolt, best guess is it is Zeithain, though such a high serial does seem to introduce some doubt, in 1926 they approached this 4500 range, but falls sort so far, but the E/16 is only known in 1927 (1926 E/11. E/12, E/13 and E/14 are recorded) and they barely made half that production (serial) range. However, it seems the most likely possibility. It would be helpful to see this WaA16 bolt as reporting markings do not give the same impression as the ability to make comparisons (fireproofs, fonts, associated characteristics, markings etc..) .