some pieces have a tendency to resonate (ring) due to their hollow shape, rather than because of their lead content - tumblers may well be an example of this. A real lead glass ring is something quite special and is probably more than just a ping.

I've had a look in Reynolds book - page 32 top picture - at what he describes as - 'Wine service with sham-flute twist, tumblers marked Walsh' -
and the tumblers do look very much like yours - with waisted and indented body and flared rim.
I'm inclined to think his aren't quite so waisted nor do they have quite the flared rim, as yours, and yours are possibly taller, but these book tumblers may well be the same as those you have found on the screen. Regret I'm unsure as to whether a 'sham flute-twist is the same as wrythen - somehow don't think it is - I always thought wrythen decoration was a substantial twist.
My own opinion is there isn't a real match here, but could be wrong - but at least you may be in the right period.
Apparently the Romans made what are called dented beakers and which Powell copied in the early years of the C20 - he also used this 'dent' on a number of his designs, although he wasn't the first in modern times to do so........... the same decorative feature appears on much art nouveau Continental glass - on into the arts and crafts years and apparently pops up in the 1930's too.
These thin clear pieces remind me of Philip Webb's drinking glasses and water jugs that he designed for Morris - they look as though they'd break if you just looked at them.