I have some good news and some bad news.
First the good news. I am the sort of person who will see something like your billboard ad, and assuming it sparks my interest, actually try to find it. That probably means trying to remember the title until my next stop where I can write it down.
So if I exist then it stands to reason others like me exist. How many? Well that's the question. But advertising is a numbers game. If enough people see it then the tiny percentage that are interested and convert that interest into action will add up.
The bad news. I tried searching your name on Amazon. I'm thinking I'd probably remember your name more easily than your book titles. I got a page full of results of things with "lake" in the title. I thought that might be because I was at the UK site. I tried the US site. Same thing. I say a page but actually I tried the first 5 pages and didn't find anything apart from a co-written religious book which I assumed was a different Steven Lake (actually it's not as I found out from your site).
I tried "earthfleet" - no results at all! I tried "The Oort Perimeter" and got a paperback (POD I assume?) and no ebooks.
I had better luck with Goodreads. I get to a list of your books pretty quickly. Though when I click the "Amazon UK" button I get to a paperback listing with a very basic cover, not the nice one you have on the US site or your own site.
So if you're relying on a billboard you're relying on something where your best hope is someone remembering your name or the title and finding it in a search later. One of the biggest places to search, Amazon, is not working for you right now. I don't know much about it but I guess you need better keywords etc. Are your ebooks actually on Amazon?
The other thing you could go for is to try to make your website the "memorable" thing. I'd go with earthfleet.net not the longer one. Though I do notice that theoortperimeter.com is available (and domains are cheaper than billboards). Then again if you want the first book to be your "landing spot" you might want to think about renaming it to a snappier, more memorable title.
Let's talk money. You say you're happy not to make any money off your books, which is fine, but that means we have no way to measure the effectiveness of your ads. What counts as a win? 1,000 new copies sold? 100? 1? If you were selling at a price you'd know when it had paid for itself. As it is you have to come up with your own measure.
What I would say is that if $3k would nearly break you then try to get that figure down. Is 6-months a minimum? Are there cheaper locations? I think -
excellent advice on MR notwithstanding of course
- you really need to try it out to see how well it works. And to do that you need to spend an amount that won't break you.
Also does the $500/month cover the cost of actually printing up the poster? Have you budgeted for a poster design?
Also look at other venues where you could spend your ad money. Online in particular.
Hope some of that is helpful - otherwise feel free to ignore!