Is there a reason you don't want to book this yourself? It is very easy o do and you would save yourself a significant amount of money.
That said, you are very late to planning for this summer. Most places in Iceland book out 9-12 months in advance in a regular year, but with the eclipse on August 12th, things booked out even further and prices skyrocketed. Your dates will still see some of that effect.
Ten days is the shortest amount of time that I would do a ring road trip. The time we did it we had 12 nights and still felt a bit rushed. We did a lot, but also missed a lot, hence we have returned many times.
If you are willing to plan it yourself, I am happy to help. If that interests you, please share the number of travelers, what your interests are, etc.