Here in FL, it usually only takes one or two good rains for a water soluble fertilizer to disappear.
Unfortunately last 2 months have probably produced only 3 good rains if that here in Martin County. But, I sure would like to see them more often.
Ok, I'll cut it up more if we are looking for more frequent significant (over 1 inch rainfall). Change it to 1/2 cup at week 2, 4, 6, 8, 10,and week 12. That should give you a good workout for fertilizing or a good psychological exam for the next office visit after talking to the plants so much.
More rain forecast.... 1/4 cup at week 1,2,3,4,5,6,7,8,9,10,11, and week 12.
Biochar and trying to make your own substitute polymer or other substrate to hold the fertilizer a little longer like charcoal, clay, etc. might be fun again only if you have plenty of time, patience, and don't mind exercise from carrying a lot of material. But unlikely worth it for most on a small scale.
I might try pulverized charcoal or bags of wood chips soaked in a homemade fertilizer solution at a latter time but have not yet.