Even that wouldn't work because as you pointed out, the entity running the script pays the gas, and that entity can not in every case have its gas balance in the partition that validates the script.
All the balances would have to be local to the partition and not shared - effectively like a fork of ETH for each partition.
And then how would a user who has his gas in partition 536 run a script that runs only in partition 1279?
Hint: he can't. Thus you would have entirely broken Ethereum with your suggestion.
edit: I'm considering the possibility of whether an inter partition transfer of ETH would be possible if the partitions merged once during the transfer and then split apart again post transfer block.
I already explained that cross-partition spending is possible (i.e. won't destroy the Nash equilibrium) only if validation of all partitions is done by all validators, which thus defeats the scaling advantages of making partitions (shards).
You even agreed with this upthread wherein you stated that validators can't decide which block to mine on if they don't validate all transactions in the block.
Edit: in case this isn't clear, let me remind readers and you that I had explained upthread that when validator that is responsible for validating only his own partition has to accept a spend from a partition he did not validate, then he has no way to know if that balance from the other partition was a lie or not. Thus he can't accept it, because his reward may be compromised if later it is shown that he accepted an invalid balance from a partition he did not validate.