5. I don't know exactly why, but there aren't a whole lot of nice supple 35-700c tires. Lotsa 32s, a fair number of 38s, but at 35mm marked you've got Compass/Rene Herse and Panaracer Gravel Kings. The more road-oriented tires tend to max out at 32mm, and Soma goes from an undersized 33mm-marked tire straight to 38mm. I don't find the Gravel Kings quite as nice as RH, but I don't like paying RH prices. I'd really like to see a Conti/V'flex/Soma SV in 35-700c.
Have you tried the Panaracer Pasela Protite? (the folding bead skinwall versions are available in 700-32/35/38 widths, among others)
Would you consider the Gravel Kings more supple?