Yes, that will always works right, but you will never get the same yield on a regular basis because it is a gamble unless you have a decent amalgam. After all, I have the same problem. An optimal reaction would be to convert the aluminum completely into amalgam, i.e. add exactly the right amount of mercury salt and then after the reduction, have no solid aluminum/amalgam left in the flask, because thus everything has been converted with P2NP.It can be Sodium Sulphate... Your reaction might not have gone all the way through. I had the same issue in the beginning, had Na2SO4 as well and others. The solution was not to rinse the amalgam (just draining the water) and also my rule for the readiness is when all the Al comes up to the surface and you can also hear a sizzling sound. There are also small bubbles appearing. This is when I consider ithe amalgam ready, and this solved the lack of reaction problem. My yield varies usually only around 50%, but never had a non-reactive amalgam since then.
It simply makes more sense to wait the first time after adding mercury salt until it has reacted completely, i.e. no more bubbles are formed, and then to start the reduction of P2NP with new mercury salt and residual aluminum that is certainly still in the flask. If the reduction stops and there is still aluminum in the flask, a further addition of mercury salt would be necessary to convert these residues with P2NP.
I think this is the way we should go, after all I have learned here.