The basic UDS design, which I believe yours is, was developed before temperatures above 300f were popular for smoking meat. UDSs were never meant to run that high. Some mods such as suggested above might be just the ticket for you.
Mine, which uses a BGE intake, has no trouble with higher heat cooks.
Jim - Another transplanted Texan
Former KCBS CBJ
Large and Medium Big Green Eggs , Black 18.5" WSM, Blue Weber Performer - Stainless, Green Weber OTG Kettle , Brinkmann SnP Pro, and a Stainless UDS. One retired Portable Kitchen grill.
Red Thermapen, Maverick ET-732, EdgePro Apex Sharpener.
Avatar is the original 1951 Weber Kettle