I would ask the OP to consider going even further and figuring out a way to facilitate some liquidity so the employees could sell enough to cover their taxes even if they don't do early exercise.
You have employees who own shares but need a nontrivial amount of cash to cover taxes. You have investors who may be interested in acquiring more shares (or the company may want to buy them itself). You have a notion of a current valuation of the shares. Broker a sale at a price that's beneficial to both parties.
What is the company's incentive to block such a transaction?
"Once our valuation rises and the cost becomes prohibitive, we’ll move to an extended exercise period model instead, where you will have 10 years to purchase your options. By that time we’ll either have had an exit (in which case you can do a cashless exercise), or we will have arranged some other form of liquidity."
The 10 year exercise window likely makes this unnecessary, but if not he says they will arrange for some form of liquidity.
Yeah, that seems good, but I'm suggesting the plan for "some other form of liquidity" be a little more explicitly stated. I know this isn't what plays well with the HN crowd, but there are other paths to success besides the explosive exit, and one of those is spending a long time building a good solid business, which can take more than 10 years.
If there's a good path to the employee owning their shares (or some fraction thereof) outright, that is more desirable in some ways than an outstanding option agreement with a ticking clock.
Post-A round makes it much harder.