My thinking is that if that screen is repeatedly clogging, the inside of your tank is pretty nasty. I realize money doesn't grow on trees, but band aid fixes often wind up costing more than we think when we do them. At 149 bucks a new tank would likely solve your problems for decades to come. You could put in a new rubber sleeve on the fill spout while you're at it and relax in the knowledge that you have solved that particular problem once and for all.
https://www.classicparts.com/1960-66...yABEgI4tfD_BwE extra capacity tank
https://www.speedshopstore.com/tanks...utm_medium=cse standard tank with free shipping. I've done buisness with Tanks inc. before and I liked them.