unfortunately, the humble tumbler is less easy to date, accurately, than a lot of other utility designs in glass, and I'd agree with your author about moulded examples being scarce from the C18, and this is probably due to the obvious fact that, commercially in the U.K., conveyor belt press moulding didn't really take off until c. 1840s, after which they were made in profusion. Not easy to say whether this one started life here, but you may well be correct.
A useful booklet is John A. Brooks 'Glass Tumblers 1700 - 1900' - there are presently a few copies on Amazon, and it's not expensive.
Before 1800 there were a variety of shapes and surface decoration in moulded tumblers, but into the C19 there seems to be more of a standardization in appearance. Certainly early C19 tumblers are often squat and almost as wide at the mouth as they are tall.
According to Brooks, one of the first indications of moulding is the appearance of star moulding on the underside of the base - presumably these were blown into iron moulds, and the absence of a pontil scar or depression might suggest post 1840. Tapering sides is a sign of earlier pieces and such examples are more likely to have a scar under the base - tumblers become more straight-sided and taller as the century progresses, as you can see if you look in Silber & Fleming (c. 1880).
Your 'feeling that this is a rare early water tumbler' should be supported up by reference to 'hallmarks' - it may be soda glass ……. oddly Silber & Fleming show acres of tumblers, one of which is a champagne tumbler ………….. I wouldn't mind a tumbler of champagne right now - I'm running the gauntlet of a 'dry January'

I think the vertical lines around the base are called 'finger bottoms', a much older decorative feature than this glass I think.
Anyway that's my opinion, and I could be very wrong, so let's see what others suggest - but I don't immediately see this one being far off from C 1850 - but would love you to prove me wrong

Unfortunately, there are few folk here who take an interest in these things, so you may struggle for decent replies, but fingers crossed.