Because I am trying to re-vamp my coaching staff, I have hit a brick wall because of this.
It looks like I'll have to sign my coordinators and my position coaches one at a time. For the position coaches, it is no biggie, because I am trawling the unemployed anyway. For the coordinators, it's pretty rough, because the good ones will be gone before I can get to them.

Awesome, I'm trying to overhaul my coaching staff too

Can you explain exactly what you are doing and what you are seeing.

I'm also re-vamping my coaches in a league.

Figures displayed on the screen pre contract offer.

Current contracts
$7,620,834
Pending Contracts
$252,000
Remaining Cash Flow
$55,127,166

Make an offer in line with existing position salaries. Select offer contract again to view the current offer, get this.

Current Contracts
$7,620,834
Pending Contracts
$378,000
Remaining Cash Flow
$55,001,166

Current contracts same -correct, those are signed, active contracts.
Pending contracts correctly updated -summation of all coach contract offers.
Remaining cash flow - adjusted downwards by the salary of existing coach.

I'm not seeing what the issue is - maybe my misunderstanding. If you can clarify the issue it would help.

re co-ordinators, can always promote from your existing position staff.

EDIT: Thinking about it, were you expecting the remaining cash flow to reduce by the amount of the existing coach ( £126k in my example ) AND the £126k offered to the replacement coach?

No, I'm having no problems with the new coaches. The problem is, the old ones still count against my cash flow. Progress has slowed to a crawl, because my coordinators were way out of whack. I pretty much have to clear the old ones before I can hire new ones. The old UI was a lot smarter about how it handled this, but the new UI, not so much.

I think it did the same in the old UI. If this works correctly, whenever FA1 runs, the departing coaches salary should come off the books. If it doesn't, then you and I are both gonna have to scramble in FA2 to fill out our staff somehow.

The way it should work (and the old UI behaved this way) is that if you are offering a LOWER salary for the new coach, the existing coach stays on your cash flow - because you aren't guaranteed that he'll sign, so the guard stays in place. If you offer a HIGHER salary for the new coach, then the coach he's replacing is removed from the cash flow.

So the cash flow uses the largest value of current coach salary and salary offer made to new coach

Makes perfect sense because it gives contingency by overestimating. If new coach doesn't sign, you'd still be on hook for larger salary.