Yea, I'd say that is a problem. I'm sure there may be some differences but in my area, I can pick up a basic SW
test kit for less than 20 bucks that comes with ammonia, nitrite, nitrate and pH. Over all, I think the liquid test kits are actually more economical than the strips because they can be used so many times.
Anyways, I realize that the nitrate reading probably makes a lot of sense to you because of the algae problem you are faced with but keep in mind that nitrate is not the only factor here...so, in reality, the main problem is that you can't yet rule out nitrates until you can be reasonably sure your test results are somewhat accurate. I'm still thinking that this might be connected to your tank being newer and/or your use of tap water. In any case though, this isn't really anything that I would panic about and I think you are doing the right thing by addressing as many different possibilities as you can.