It’s hard to give concrete answers without understandimg the business context but here are a couple of ideas to think about

1/ If you can’t scope work yet propose a discovery phase in which you’ll do whatever you think is needed to get to a scope of work. More importantly in this phase work out the ROI for their business of doing the work. You should be able to bid this fixed price - 3 of you for x weeks/months.

2/ Day rate consulting is safe but you may not be able to capture a fair share of the value you create. Pricing based on a percentage of their ROI over 3 to 5 years may get you a better deal.

At the end of the day what you are doing right now is sales. The companies budgets, your competition, how they like to work etc will all be big drivers of how you can operate. Make sure you understand all that.