I'd do it for time and materials, unless you are very confident about your estimating skills, which you are obviously not. Around here gardeners charge £25 an hour or more. Include all the hours you have already given them. Mate's rates £19.99?
Remember the basic rule - the client is always wrong. What they are proposing sounds ridiculous.
Our new house had a small but hi-spec garden somewhat similar.
We didn't know it was there until we cut down the Leylandii "hedge" which had become a small copse, and then hacked through various other thickets. Uncovered a network of flower beds with stone edges, concrete kerb stones, beds of shingle, stone and concrete pavings completely overgrown. A bit like discovering a small lost city in the Amazon jungle!
The point is - they were trying to construct some sort of exotic mediterranean designed garden but completely unaware that it will cost a lot to start with and involve intensive maintenance.
A good garden is something which evolves over time. Start with what's already there and well established - it should be a lifetimes project - step by step a bit at a time.