There are a lot of premium / hybrid solutions out there which may offer you the balance and higher price points you're looking for. Toptal (a16z) does temporary placements and is one such hybrid model.

There's also gun.io (actually, think they pivoted slightly), ooomf, hackerlist.net, 10x, etc.

Disclaimer: I am a founder @ Hackerlist.

Having run and advised consultancies for a while, and having been an employed engineer, I'm happy to discuss the tradeoffs of each in detail, assuming there's interest. In terms of getting clients, I do think it helps working with another organization to increase your intake, even (especially) if you run a small consultancy/agency.

Alternatively, happy to answer questions or help make intros around SF if people prefer personal interactions <m@hackerlist.net>