I've used the Circa 1850 with success on many stocks, a few of which were very heavily coated with a gloss finish of some sort. I usually use a scraper, as mentioned by petew, lots of paper towels, and steel wool for really stubborn bits. I find it easier to work with the "gel" version of Circa, and after each bubbling, scraping, and wipe down, I rinse the stock with hot water in the laundry sink.
Dry wiping after the rinse shows any areas of remaining old finish that need further treatment. No need to worry about the wood absorbing moisture. Just leave it for a day or two before starting to apply the new finish.
No soft brass brushes handy? Old toothbrushes or new cheapies from the Dollar Store can be used for cleaning out checkering. I usually tape off the checkering when doing the final cleanup before the refinish.