As discussed in yesterday dev call, I open this issue just to be sure to track it.
Right now the future job is created and sent downstream right after a new block is found, and miners start to mine on it right after the SetNewPrevHash message is received downstream.
We could surely manage future jobs creation more cleverly, some ideas are:

• build a future job which is based on a template containing txs with less fees taken from the mempool (which most probably won't be taken by other miners as well)
• build a future job speculating on the fact that the current template which the miner is mining on, will be the winning one
• others ..

For reference I suggest to have a look at https://github.com/stratum-mining/sv2-spec/blob/main/05-Mining-Protocol.md#514-future-jobs