Unless you can get to the grub screws from below the cartridge they will not work.
There is one other solution. Roberts makes a product called "MAX GRIP carpet" Home Depot sells it. It is an extremely strong double sided tape. With the stylus guard in place place the cartridge on a piece of the tape then trim the tape to the cartridge with a carpet knife or sharp scissors. You will have to figure out the proper location and angle of the cartridge in the head shell before sticking the cartridge down permanently. DO NOT remove the backing tape until you are ready to attach the cartridge permanently. To get the cartridge off you will have to slip the edge of a sharp knife under the cartridge and gently pris it up. Do not try to pull it off with your fingers.
Mounting another tonearm is worse than drilling out the head shell. Remember, anyone who wants to use this turntable with a modern cartridge will have the same problem. Drilling out the plastic is not a problem for someone who knows what they are doing. You have to use brad point drills at slow speeds so you do not melt the plastic. This should only be done in a drill press.
Another solution would be to modify the end of the arm installing an SME socket so you can use any universal head shell. That is a bit more complicated, but it can be done. Anything can be done if you throw enough money at it.
And the last and easiest solution is, a Grado Gold or Silver cartridge will fit right on, screws from below.