@pete_c:
Before I get to the solution I would like to point out as mentioned in my post, I was coming from a working solution with the predecessor to this doorbell, specifically the Hikvision DS-KB6003-WIP. Needless to say I was tearing my hair out when it's successor the HSDB2A didn't just work with my setup plug & play style. I typically solve my own problems but I posted here in frustration & desperation - so thanks for taking the time to researching my model chime & trying to help.
A little more background about the RCW35
Not explained in the excerpt from the RCW35 manual you posted is that in that configuration the doorbell takes in 16VAC from the transformer and steps it down (in half) to 8VAC for the connected doorbells. Similarly 24VAC gets to reduced (in half) to 12VAC.... this quirk made the Gen1 tricky to get working with this chime particularly with the 'power kits' being in scarcer supply back then -- really only ring had just started making them back then.
TL;DR #1:
Digital Chimes are a pain. Honeywell models in particular.
TL;DR #2:
The HSDB2A appears to have a slower charging battery/capacitor solution than it's Gen1 predecessor. Even wired & powered correctly it may take some time until is charged (1-2 hours was my experience) for it to start activating the attached chime (at least if its digital) when the button is pressed.
This quirk may lead you to falsely believe (as I did) that something was wrong in the wiring configurations you try even when you've wired things correctly.
Additional Anecdote Detail, Ranting & Final Wiring below:
I had started by configuring & flashing the doorbell on the bench minus the chime and then later tried to install it in its final place. Minus the chime of course everything worked as expected.
I of course had more difficulty getting it to work in practice. Now I had two different sizes of 16VAC transformers, a 24VAC transformer and 3 different power-kits on hand that I tried (The included one, honeywell's own 'skybell digital doorbell adapter' and the simple diode that did the trick for me on the Gen1 devices. With all of these component options on hand when something didn't work I never waited long enough before trying the next configuration.
I had tinkered with the doorbell all week and stayed up late the night before halloween trying to get it working. After work on halloween-proper I quickly restored the doorbell/chime to a configuration that I knew would let it work as a camera so my dahua/lorex NVR could record the night's events -- We were going to leave a large bowl out for the visiting kids while were chaperoning our own and wanted to see which kids would invariably empty it when they thought nobody was watching.
About an hour later after we got back home with a own kids low and behold we were surprised to hear that the doorbell had started to activate the indoor chime. At first there was a 3 second or so lag but it reduced further to somewhere under a second. Relief & Vindication!
Final Wiring: