I could (I mean in theory - practically, I'm not technically proficient enough to do so), and in fact one of the most promising web browsing agents I've tested is director.ai, which just writes Stagehand code on the fly to achieve the objectives you give it. Unfortunately it can't be invoked via API yet, so doesn't work for my use case.

Honestly, it takes such a relatively small amount of time that it makes sense to just do it myself until there's an agent that can easily handle it; I'm really only spending time trying to automate it now as a test of AI capabilities. If I actually wanted to get it automated tomorrow, the most time-efficient way to do that would just be to involve a VA from somewhere cheap for the work I'm doing.