i had a weld on the top of the catalytic converter come loose and gave me similar issues. crawl under when its on ramps and start banging on exhaust or suspension / driveline stuff... maybe engine mounts going bad?
2003 C5 50th
2000 Silverado Z71 - bolt on's, work truck
2000 trans am - "Nevermore" 353 hp / 358 tq, int/ext/eng/susp/etc... always working