Do you think the circuit I have drawn has any glaring weaknesses?
U2B is duplicating the job already done by U3A.
I can't really articulate the difference, but an original 6G15 doesn't sound "uncolored" with respect to the Dry signal. I have a 1965 original.

I have been unable to find an ERIII for sale ...
There are 2 of them for sale on Reverb.com right now (plus a few Echo-Reverb II examples). Kinda pricey though.
As to whether it is better or not, I really cannot say but the story I have made up in my head from whole cloth is that ... the added expense of two (rather than one) tube is some indicator of a better quality circuit in the later versions. ...
The 7199 is a relatively uncommon and expensive tube, and the 12AX7 is widely available from everyone.
Two 12AX7 triode sections replace the pentode-section of the 7199, and afford a spot to insert a T-filter for mid-scoop between sections.
One triode of the other 12AX7 replaces the triode-section of the 7199.
The other section of that tube seems to be used "because it is available" as a grounded-grid amplifier, in the same way the 7199's pentode-section was used in grounded-grid mode for the "Reverb" feedback.
If I were going to buy an Echo-Reverb, I would get the "III" version, only because I have plenty of 12AX7s and don't want to be locked in to more expensive 7199s.