Never heard of anything like this. You need specific antibodies for this job, and I dont think any company is producing ab for AA WB. However, one thing you may think of radioactive imaging like methionine labelling with 35S but I dont think you can use it for your system though.

I can't see how this would work. Amino acids will all run at the dye front of SDS-PAGE and will probably pass right through the membrane. Fluorescent derivatization and HPLC (or UPLC) is the standard method for amino acid analysis.

I published an enzymatic method for detection of methionine using the enzyme S-adenosylmethionine synthase (MetK).

Article A High-Throughput Absorbance-Based Assay for Methionine Prod...

I think an analytical machine like HPLC will be needed