I am still confused with what you want. I guess you only want to update the web value when Money is bigger. Also set Money to the webvalue only at the start. Try these two method
1) add/change a couple of conditions
On start of Layout+int(WebStorage.LocalValue("TotalMoney")) > 0: Set Money to int(WebStorage.LocalValue("TotalMoney"))
Money bigger than int(WebStorage.LocalValue("TotalMoney")): Set Local Key "Total Money" to Money
2) Try to switch the order like this and put them at the bottom of the event sheet.
Money not equal to int(WebStorage.LocalValue("TotalMoney")): Set Local Key "Total Money" to Money
int(WebStorage.LocalValue("TotalMoney")) > 0: Set Money to int(WebStorage.LocalValue("TotalMoney"))