Morena – these ‘projects’ – depend on the terms of your contract with your client, whether all ideas are theirs or you are free and clear to go forward. My belief is that the client would think they were theirs, and probably have a contract with you to that effect. Have a look at your contract and regardless, you should talk to them about it, given it is a major client of yours.
In terms of funding, there are a range, if the projects are r&d based – then Callaghan has some getting started grants, but maybe not this high – you could try angel investors or crowd-funding. The best type of funding is from customers, can you get them to give you funding early?