Thanks for all the replies.
I tasted the cheese today, since one part of the "character" broke off when I was turning the cheese (not fault of cheese texture, but my own accident). It tasted surprisingly little salty, so I could add some more. Of course now the cheese is already a bit old, so I wonder how the time between pressing and brining would affect the result. Well, maybe brine it just a little bit.
It tasted good, actually it already tasted pretty much the way I was hoping for the end product to taste. So I'd like it to age for about a month for the texture to develop and dry it out a bit (by brining then, I suppose).
Actually, after accidentally breaking + tasting, I don't feel like it as loss at all.
siegfriedw, I was actually thinking about adding some white or blue into it when I noticed the texture. So maybe it would've made a fine camembert. I think my milk and rennet were fine though, since the rennet worked fine just a few days before, and it should have 2 years before the expiration date left. The milk was fresh from the store, pasteurized. Never had any bad milk from the stores.
Debi, thanks for the supportive attitude.
I'm sure this will turn out fine, just the steps are different than I thought. Somehow it hasn't gone to my brain earlier that brining expells moisture from the cheese. I feel stupid, since that seems obvious if thinking about the chemistry.
Francois, you guessed right, I was going for creamy havarti, and that's why I added the cream. Although, at least in Finland the average raw milk fat percentage is around 4,2 and my milk is 3,5 (the highest fat rate commercially available), so I shouldn't be much above the raw milk ratio.
Actually a question just popped into my mind about whether "whole milk" means the same fat percentage everywhere... different pastures, etc.
The time between adding rennet and cutting the curds was about 30 minutes. I thought I got a pretty good clean break. The milk+cream seemed to coagulate a bit differently if compared to just milk, though. I wonder if that interfered with my perception of the seemingly clean break.
And no, it did not setup like concrete (not all of it). A part of the curds stayed in an easily fracturing form, where you could still see the square form of the original cut sides. I tried to cook the curds to firm them up, but at the end they were still pretty soft and since it was a new recipe for me, I coudn't know if that was desirable or not.