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I’ve been rocking the orient esteem open heart recently. (this one here [link]) I think it’s a great affordable automatic that doesn’t break the bank. I’d recommend picking up a replacement strap though.
This might not quite be what you're looking for and it's a little over budget, but Orient is a well-recommended brand and has a very good reputation.
I would like to present these to you for your consideration. I have owned a Skagen before and while they are decent watches they are over priced for what you get. These Orients are well built and are a very accessible entry into the wonderful world of mechanical timepieces.
fossil has a wider selection of open hearts but an orient will last you much longer - it has far better build quality
Honestly the only type of affordable tourbillon is going to be Chinese, but I'm really not sure what it out there, as Chinese watches don't appeal to me. Does it have to be a tourbillon though? There's some pretty interesting open heart watches like this Orient, and while it isn't a tourbillon, it does have a similar aesthetic. Here's a few more OrientStar models. And a little more expensive is this Frederique Constant Open Heart at 1500
In stock and MUCHHHHHH cheaper
Not sure if you bought your watch yet, but Amazon.com has a different variant of this watch on sale right now. There's a 20% off coupon bringing the price down to $100USD. Shipping cost me $23USD.