Sara,
I'm no expert but I do have some thoughts!
First off, I think that you are right to be suspect of the archivalmess of bristol board. I suspect that most of bristol board sold is made with relatively cheap pulp which is not archival.
In my view, if a paper does not say that it is made from alpha-cellulose or from cotton (rag) then your can be pretty sure that it is made from pulp containing lignin and therefore it is not particularly archival even if it is labeled "acid free". Paper made from lignin free pulp is a selling point and manufactures never forget to mention this in their descriptions. Thus if a papers description doesn't say it is made from alpha-cellulose or cotton (rag) then it is not likely archival. The only cotton (rag) bristol board I know of is Strathmore's Series 500.
An additional factor against the archival-ness of bristol board is the fact that it is made by gluing sheets of thinner material together. The glue used is an unknown in terms of archival-ness.
Also an unknown factor related to archivalness is the likely presence optical brightening agents (OBAs) in most (all?) bristol board. OBAs are compounds added to paper to make them appear very bright white. These compounds decay under exposure to light causing paper containing them to yellow over time. Thus papers containing OBAs are not considered archival. I imagine, but do not really know, that the difference in the blue tones you note are related to the difference in the "paper white" between bristol containing OBAs and a good paper such as Arches which does not contain OBAs.
As for other smooth papers to try, I would take a look at the many hot pressed watercolor papers available. They are all pretty smooth although many (especially the cotton papers) have much softer surfaces than bristol board. In general papers of the same weight made from trees (both cheap sulfite pulp and alpha-cellulose) will feel somewhat stiffer than cotton papers. You can get some watercolor papers in very heavy weights if you are interested in replicating the "heft" of bristol board.
Specifically, you might take a look at Fabriano Studio hot press watercolor paper it is a mixture of alpha-cellulose and cotton and has a very smooth, fairly hard surface, not unlike bristol board. It comes in both 200 gsm and 300 gsm and is very reasonably priced. I get mine from these folks...
https://www.acuitypapers.com/Studio-Watercolor-p/119-0670.htm (no connection to these folks other than as a satisfied customer).
Additionally, you might take a look at the papers designed specifically for platinum printing... Hahnemuhle Platinum Rag, Bergger COT and Arches Platine. These papers are all quite smooth, 100% cotton and fairly heavy. They are not inexpensive though!
One last paper to consider is Cranes 90 LB cover (wove), again very smooth with a fairly hard surface. The natural white is fairly warm but OBA-free. This is a fairly hard paper to find, but it works well for alt process printing.
Hope this helps!