Building insurance for timber frame construction, impossible?

Yes, Check 24 only shows a single tariff, and quite overpriced at that. That’s too little choice for me. Verivox does offer more options, but strangely, the tariffs there are more expensive with the same information than if I go directly to the insurance company’s website and get a quote there. Probably different assumptions are being made, but I can’t select them myself. I’m going to call them now, because completing it online is too risky for me. In the end, the assumptions might be wrong, and then I have no insurance coverage.

Are these insurance brokers also independent like financial brokers, or do they always belong to a specific insurance company?

General agent/main agent = usually works for one company
Broker = has contracts with various (not all) companies

Brokers usually do not act completely independently either, as they normally receive commissions for their mediation and renewal commissions for ongoing support.
The advantage of the GA/MA = they often have good contact with their insurance company and can therefore resolve questions directly via the “hotline.” The broker pretends to do this as well – but who really has equally good contact to 50 different companies?
Cynics claim that the broker still tends to choose an insurance that pays him the better commission. Even if only so that 1-2 years later he can suddenly pull a much cheaper insurance out of the hat, from whose conclusion he again earns something.

Fee-based advisors would act completely independently. They charge a fixed hourly rate for their advice – but according to the law must waive commissions and the like. This is contractually agreed with the insurance companies – if this is not possible, they would have to pass on any received commissions to the client. Since the fee-based advisor receives no commission at all, you can assume that he will find the best insurance for you. If you do not conclude a contract, you still pay the hourly rate.

This model has hardly established itself in Germany so far. One reason for this is that the average citizen is not used to paying for advisory services and believes that this advice should be free of charge.
Years ago, Deutsche Bank tried to introduce such a model at banks. After massive public outcry, it was scrapped again. Currently, I only know of one bank in Germany that offers fee-based advice.

Are these insurance brokers also independent like financial brokers, or do they always belong to a specific insurance company? I generally don’t know much about insurance matters. I need to read up on it first. Thanks to you all in advance!

Insurance brokers are usually always independent of any company. Of course, it may be that some brokers limit themselves to fewer companies. Agents, on the other hand, are generally tied to an insurance company. Whether the portals are the right choice in your "special" case, I would doubt, as the evaluation criteria there are presumably not sufficient.

Yes, I have already noticed that everything is pretty much designed for the standard case. With exotic construction methods, you don’t get very far. It is also strange that with the same inputs on portals and directly with the insurer, very different premium amounts come out for the same tariff of the same insurance. Could it be that brokers receive some kind of "special discounts" and that it is therefore cheaper to conclude through a broker than to go directly to the insurance website and request a quote?