Stop soaking him. It's a stressful act and stress can actually lower the immune system.
RI can take from around 30 days to 3+ months to show signs of improvement.
And $800 for a culture is absurd. Should be around $200 at the very max.
I do agree with your vet that a lung wash+culture should be done. But if you choose to do that, I would go to a different vet to do it. Your vet is overcharging several hundred dollars.
An instead of saline, you can try F10 for the nebulizing treatment. Just make sure it's diluted correctly.