It's a game of chess, not poker.
What do you do now? What do you show them? There's many win conditions.
Sign up for their service in return, tell them, may the best man win. Think also that winning is for the benefit of your customers, and for each competitor to be the best possible.
As long as you're not competing directly against yourself ie. stolen IP, it'll be fine. On that note, you ought to conceal some amount of your source in some way.
Don't be completely open source, have some small thing that can't be copied. The intent of being open source counts. One good way to do this is to have a more efficient algorithm than what's available publicly (talk to me) and then your open source offering has the regular algorithm, but your closed source advantage is a much more efficient algorithm that represents a competitive advantage. Like say multiplication, simple example, suppose you're working with crypto and want fast multiplication, if you can do it faster with some hot algo, you aren't forced to share that, users copying your source can use the run-of-the-mill algorithm. It's the same thing, exact same thing, same input same output, just that you happen to have a faster algo you keep to yourself. You don't even have to tell people! Still open source! Anybody can run all the code!
Because it's strictly necessary to have IP, or tech if you want to call it tech, that can't be copied directly and trivially. Mark Lemley at Stanford says so in his IP law class: "Suppose there's two competitors, one does all the work of creating or inventing something new. The other just copies it. Costs nothing, it's a sure thing. I'd love to be that guy!" It's not as unreasonable as the internet makes it seem.
So you just have to know the system because there are gotchas, like with any law that tries to be fair. So for one, for USPTO, deadlines are deadlines. Death. You missed the deadline? You cannot ask forgiveness for your mistake, they're completely unsympathetic (and it's because people try to hack them so hard). So actually becoming familiar with IP law, and then routing your business in the direction of what you can protect.
Analog is another form of protection, that's very common in high-precision manufacturing in Germany, basically you have an industrial Excalibur in your factory that your competitors don't have.
And what I would do is, sign up to your competitor's service in return, and try it out. Also: try to differentiate somehow. I created a theorematic pricing algorithm and the idea was you just can't charge the same price as a bunch of other people, you have to be different, undercut or mark up, whatever it takes to be alone in the price curve. And when you do go up or down, adjust your product accordingly and according to the specific needs of customers who want to pay that price for it.
That algo is also for sale.