Personally, I have always found harder to finance and than creating opportunity.
It is quite "easy" (once you have the right value proposition and target customers) to sell but getting paid is way more difficult. Most small business are dying not because they are not selling, but because they are not getting paid early for their work and finally lacking liquidity for their operations.

So funding is a bit like getting paid in advance.

What we usually do is split the total bill in bits to be paid out gradually based on progress and well defined target.

I have seen your situation before with other customers. What they did was to start developing the product with the budget they had focusing on the most interesting part and then they went with this half finished but functional product to pitch investors. And this how they got the missing part of the funding.