My american standard low flush toilets are clogging weekly. What can be done to resolve this problem?

Toilets wear out from mineral deposits. Fixn may cost more then new. Googl used commodes first

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Your vent stack may be clogged. The pipe that goes up to the roof. Let's air into sewer pipes when you flush. A birds nest or something can do it.

Check your water level it should be about 1/2" below the top of the overflow pipe. Also if its American Standard the flush adjustment on their flapper valve is very finicky (the type with small round chain links) if its too tight or too lose it will not flush properly.

Welcome to the world of 1.6 gallon flush toilets. You have already done everything that can be done to help the problem and no you are not the only people having this problem. This is just the beast!
They have had this problem with these 1.6 flush toilets from the get go and have come out with power flush toilets to fix this but hold on to your wallet. There are some toilets out there that work better without the power flush made buy American Standard and Kohler but they will run you more then the Jacuzzi.
Sorry I wish there was a better answer to this.

If you have that thing off, take it outside and put it up on saw horses, fill the back with water and flush it, see if it is still slow. Then get your kid to reach up there and get his toys out if it doesn't flush. You might have to do it a couple times. Then if it does flush, you know it is clogged down the line or something is blocking the vent. Got squirrels? Check it out.

your float is stuck

sounds like an old tiolet (3.5 gpf) my best answer is to replace with new fluidmaster! (lowes or homedepot) easy fix!