A phosphate reduction using a phosphate remover is not necessary if you kill off the algae by shocking the pool and then maintain an appropriate FC for your CYA level as shown in Ben's Best Guess CYA chart.

First of all, I wouldn't trust the pool store readings, especially the CYA reading. Get your own good test kit: the Taylor K-2006. If your CYA level is truly 50 ppm, then your FC level probably dropped below 3 ppm for a time then algae was probably able to grow faster than chlorine could kill it so increased chlorine demand greater than your SWCG output, but I suspect your CYA level may actually be even higher.

Note that pool store and SWCG manufacturer recommendations of 1-3 ppm FC are NOT sufficient to prevent algae in typical pools with higher CYA level -- usually around 60-80 ppm CYA in SWCG pools as recommended by most manufacturers. You need an absolute minimum of 4 ppm FC in such pools and possibly higher (Ben's chart shows 5 ppm minimum).