For courtesy 'notifications' I found that a monthly budget report (which we also did) can cover that for the High Council. The communication around a planned, pre-approved budgeted activity was such that there was rarely a question about items coming in. Again, remember, it did require we do some really good planning, but went along with my mantra.
It's a budget, NOT an expense account.
Expenses are approved in a manner described in the OP, reimbursements, in my mind serve a different function, it's already been technically approved for purchase by the org leaders by the nature of the budget being approved by the Stake Council and Stake President, only the reimbursement, per the check issued, has need of approval of either the SP and/or the Bishop.
For example, a the Stake Young Women's Secretary submits a reimbursement request for paying the DJ for a Stake Dance. Is this something that the org leader needs to 'approve' will it be 'not approved'? or for that matter, for that same Stake Dance, another member of the Presidency submits a reimbursement for 'treats' for the Stake Dance. I'm not going to ask the YW President to make sure that this is an approved expense, I'm pretty sure that members of her presidency didn't, on their own, hold a rogue stake dance and try to 'sneak' in approvals for a DJ and treats. On the other hand, if they were to submit a reimbursement for 'Dinner with other Stake Young Women Presidencies in the area' that isn't on our list of approved budget items for the Stake Young Women org, I'd reach out to both the stake president and stake young women's president asking what's up with that... then the stake president would likely say, oh ya, I forgot to tell you I approved that.
If items came in that were seemingly being treated like an expense account I alerted the Stake President and a conversation happened. But overburdening a process, particularly one at the stake level where you're not necessarily processing financials each week like in a ward only leads to people being put in financial burdens, and avoids the member asking that we also pay the interest charge on a card because a high councilman sat on a paper form.
I can see this being a bit tighter at the ward level, though good planning really does the trick there as well.
“A long habit of not thinking a thing wrong, gives it a superficial appearance of being right, and raises at first a formidable outcry in defense of custom.”
― Thomas Paine, Common Sense