i only just started using mzscript last week but i think doing it like this should make it work in the order you want

*Script bang !button1
*Script exec !thebangyouwanttoexecutefirst
*Script exec !thebangyouwanttoexecutesecond
*Script exec !thebangyouwanttoexecutethird
*Script ~bang

thing is though i assume that your execute bang has all the sub bangs in the order you want them and i always thought that execute runs the bangs from left to right.
on a few occasions i've found using a pause bang helps on long executes, i guess sometimes some things need a tiny bit longer to do their thing