The question is essentially this: If I boldly apply a plain 15V/5A source to a device designed to QuickCharge 3.0 proprietary specifications, will my device charge?
The answer is: likely not. The QC process starts with the default 5V level, and then device request higher profiles by manipulating with D+/D- wires and setting certain DC levels. This is a sequential process, and if the initial handshake fails, the device will likely not engage higher charging rates and consume more power from charger.
The second question is, will the bold 15V5A fry my QC3.0 input circuitry? The answer is "who knows", unless the device datasheet explicitly says that it is tolerant to any voltage up to 20V regardless of QC presence, or the schematics of the charger section inside your device is known, with all related datasheets.
You have made the right choice to use 5V only, please continue to run it in this mode for your safety and safety of your device. However, in all likelihood, your device will take only 500 mA and charge very slowly, if at all.
The USB Type-C doesn't work as you described. The load of ideas how the port should opreate (as dual-role port) is described in the original USB Type-C specifications, which are freely available from USB.org, as part of entire USB 3.2 zipped package.
Initially none of Type-C port will have any voltage on VBUS, so you can't use it as detector who is provider, and who is consumer. The role of a port is determined by pulls (up or down) on CC pins. And the CC wire goes from one port to linked port over C-C cable. Once the right combination is established and recognized, the source will put out VBUS, and the consumer will take it. For details please examine Section 4 of Type-C specifications, all variants of connectivity are pictured there.
Best Answer
All answers are severely misleading. You can't get any other voltage than the default +5V without Power Delivery negotiations.
Now, the Power Delivery specifications (614 pages) are as long as the entire USB 2.0 specifications (622 pages). The negotiating protocol involves hundreds of messages over 300 kbps link that is as complicated as USB, and the number of protocol states/stages are in order of 200. Starting from a background of bare Type-C pinout and even buying specialized IC is a far-far complex task. The mentioned specialized ICs are providing only the physical level interaction across CC links, and at most provide packet service. The entire negotiation protocol and "policies" are implemented over a general purpose MCU, and implementation of all these crazy polices takes thousands lines of code ("just as your laptop does"), so an advice to DIY the protocol interface at OP's level is misleading.
However:
The board has at least 5 ICs including ARM 32-bit MCU chip, so it will be a challenge to make another one for this price tag.