These are soooo comfy (anything conti Supersonic is) but the carcass is so thin, problem is they’ll puncture if someone so much as sneezes nearby so not really an ideal tyre for a commute in my eyes.
Try a bit less pressure first before splashing out cash would be my suggestion, but bigger volume tyres will be the best option run at sensible pressures, you’ll get so much more small bump comfort from tyres than you ever will from suspension. The full armoured tyres are great for reliability but the carcasses are often quite stiff so worth running them softer than you would think to get some comfort back unless they start getting too draggy.
As a left-field recommendation Michelin Wild Run’r tyres in 26×1.4 flavour have been a really surprising tyre for me, fast, very comfy, grippy on tarmac and hardpack for a slick, and when I bought them only a tenner an end, no punctures in the last 12 months of commuting and lugging a trailer around for shopping.