Seems actually a better use case for paying in stock (compared to regular employees). You only work a short time for them, so you can spread your bets more like a VC, and your influence can have a decisive impact on their success, so it's not just a lottery ticket.
Even if we assume that they are willing to part with stock for consulting engagements, can you afford to wait years to get paid?
Can you afford to pay taxes on that income this year? (to you it's paper money that might never to turn into real money; to IRS it's as good as payment in cash).
Restricted and illiquid shares are rightly valued at a discount to the same shares with a liquid market, so while you pay taxes on them, it's on their fair market value (which can be low as above).
