Third gear synchro on the TR6060 is genuinely one of the known weak points on these boxes especially when the previous owner was enthusiastic with no lift shifts so you are probably diagnosing this correctly. Try the fluid change first because it genuinely does help on these transmissions and costs almost nothing compared to a rebuild, Redline MT90 specifically has a good reputation for smoothing out TR6060 synchro grind in the early stages. If the fluid change makes a noticeable difference you have bought yourself time, if it does nothing then the synchros are too far gone and the rebuild conversation becomes necessary.

The TR6060 is actually a very rebuildable unit and a competent transmission specialist with manual gearbox experience does not need to be a Chevy dealer to do this job properly, the Tremec design is well documented and the synchro replacement is straightforward for someone who knows what they are doing with performance manual gearboxes. What you want to avoid is a shop that pulls the box, replaces only the third gear synchro rings, and puts it back together without inspecting the other synchros and shift forks for wear while everything is already apart. If the previous owner was genuinely hard on this gearbox the damage rarely stops at just the one gear that is currently presenting symptoms. Ask any shop you consider specifically what their inspection process covers while the box is open and how they handle finding additional wear beyond the presenting fault.

Pretending it is a race car thing only works until the grind becomes a crunch and at that point the damage inside the box accelerates quickly and starts affecting components beyond just the synchros. The hitting a wall feeling you described when shifting at higher revs is telling you the synchro is already struggling to match shaft speeds before engagement which means it is working harder than it should on every single shift even the ones that go in cleanly. Getting this sorted before it gets to that stage protects the rest of the gearbox which is in good shape and keeps the repair cost at synchro replacement territory rather than something more comprehensive. The TR6060 with fresh synchros and a good fluid in it is genuinely one of the nicest manual gearboxes in a modern muscle car and getting it back to that condition is absolutely worth doing on a car you bought specifically for the driving experience.