This strikes me as a chaotic scenario, where the appropriate response isn’t apparent, but cost of delay could well be catastrophic.
The risk is not just building a sub-optimal solution, but eroding your fundamental product market fit.
First principle of triage is to stop the bleeding. You do that by building customer confidence that the solution is coming.
But as far as story point estimates go, seems to me the key points are:
There are some potential solutions that could take as little as 3–4w. So somewhere between 4w and 5 months
There are no clear winners
Story estimates will allow you to understand the relative cost to release a particular solution.
But development cost is not nearly as critical as lost customers. It’s the incision to repair the bleeding artery.
Also time to release is not the relevant metric. Time to confidently communicate to the market the forthcoming solution is the right metric.
IMO story-level estimates are useful, then, only as far as they tell you the cost (in time) to reliably _exclude_ each solution. And really, you’re looking for the fastest path to exclude all but one solution.