You mentioned "overdoing it with the tripod advice" and I get that, but most people skip the real fix which is just using burst mode. I shoot handheld all the time and burst mode saves me from shaky hands by letting me pick the sharpest frame out of 10. Have you tried that instead of always reaching for a tripod?
Agree completely, burst mode is a lifesaver for handheld shots especially in low light. I basically live in burst mode now and it's crazy how much sharper my photos got without buying any extra gear.