At the last seminar I attended on pain relief in cattle (within the last 5 years)... the presenter mentioned aspirin... but said it was so close to ineffective that they no longer recommend it.
Pulled this from the abstract of a published paper on administration of aspirin to cattle (ca. 1975... almost 50 years ago, now... so consider accordingly):
"Despite slow absorption (half-time of absorption, 2.91 hours) of orally administered aspirin and rapid elimination (biologic half-life, 32 minutes) of salicylates, oral dosage of 100 mg/kg every 12 hours maintained serum salicylate concentration greater than 30 mug/ml, which was considered to be therapeutically effective."
Based on typical adult human aspirin tablet containing 325 mg, you would need to give 1 tablet per 7.15 pounds of body weight, twice daily, to achieve that target 30 mug/ml serum level. There are 240 grain and 480 grain aspirin boluses made for administration to cattle... but I've never used them... I never used aspirin while in practice. Perhaps Ken or Buck can weigh in, as I'm blathering strictly as an academic on this point.
An appropriate dose of Banamine(flunixin meglumine) - given INTRAVENOUSLY - has a minimum slaughter withdrawal of 4 days (7 days is better to ensure no residue above accepted limit). Intramuscular or subcutaneous administration is not an approved route for Banamine; therefore, there is no established slaugher withdrawal, if flunixin is given by those routes. FARAD (Food Animal Residue Avoidance Databank) indicates that a single IM dose of banamine has minimum 10-day recommended slaughter withdrawal (if given at 1.1-2.2 mg/kg in volumes of not more than 10 ml per injection site) - last time I looked before today, the recommended withdrawal time for one IM injection was 30 days. If you give more than one dose IM... it could take 60 days or longer for residues to clear.
Flunixin use is one of, if not THE, leading causes of condemnation of cull cattle carcasses due to violative tissue residues... because folks give it IM and then ship that lame cow for slaughter the next week, because she's not better. (Effective half-life of Banamine in the cow is about 9 hours)
I've used meloxicam in calves for post-procedure analgesia following dehorning, and some folks give it when castrating. But those calves are months away from going to slaughter, so withdrawal is not an issue.