The only ones available in my market are 20% down or more. Usually that is done in land equity (IME). Ideally you own the land outright and they just count the full value + any improvements towards the 20%. If not, you need to bring cash to closing.
I can't help with a bank in Flathead, but I can tell you I struggled last year with finding a local bank here even willing to do a construction loan at all. Everyone's staff was so eaten up with refi's, that they just didn't have time to deal with with the relatively low return for that product, and just paused doing them. Hopefully that has eased somewhat. I ended up using a national lender (Prime Lending) and then going back to a local credit union for the long term. I wasn't thrilled with using the national lender... they had a local originator, but then I had to deal with someone down south for the loan draws, and communication could be a challenge at times.
I've done a couple different types of loans. The first was geared towards the "owner-builder" and allowed as many draws as needed and reimbursed to us directly from receipts/invoices. It was good when acting as the general contractor, but involved a lot of paperwork. The second was geared toward using a licensed General Contractor and allowed a set number of draws (5 in my case) and paid out to the GC directly. Make sure you know what kind you want, and how they work.
The construction loan process is a huge amount of work. I've sunk hundreds and hundreds of hours into those things!
Yk