As a designer, I think you're going to have a very hard time finding someone who is interested in full time and also talented. You're drilling in the right places but the wells are dry. Right now every designer in my network is either working at a top tech company or has a lucrative consulting career.
Talent is in extreme scarcity, lots of people have personal projects, and that means they aren't going to jump at the chance to work on something full time. Even if you have healthy funding. Exceptions made for instances where the founding team all love working together and are getting healthy equity.
A compromise is going to have to be made. Remote is one option, but I wouldn't recommend it unless it's with someone that is particularly good at working remotely. I do it a lot, but it does take practice to learn how to communicate effectively & maintain momentum. Part time consulting is definitely an option. Though the time per hour can me more costly, it can also be more efficient. The last option would be finding someone that you can teach. Assuming you know what you want and have good taste, you could find a less experienced designer with a lot of talent and invest in their learning process. If you don't want to do that yourself, you could also hire an experienced consultant that would complete the initial design tasks to set a tone and then stay with you to train the fulltime designer.
Good luck with the search!