Hello,
First, contacting Apple Support directly is likely your best next move.
I’m assuming your device is intel-based since you only are needing to use D and no other combination. If not, ignore this answer.
This article could be relevant for your situation.
recoveryOS and diagnostics environments for an Intel-based Mac - Apple Support
“If an error has occurred in the launching of the local recovery or diagnostic environments, the UEFI firmware attempts to download the images from the internet instead. (A user can also specifically request the images to be fetched from the internet using special key sequences held at boot.) The integrity validation of the disk images and chunklists downloaded from the OS Recovery Server is performed the same way as with images retrieved from a storage device.
While the connection to the OS Recovery Server is done using HTTP, the complete downloaded contents are still integrity checked as previously described, and as such are protected against manipulation by an attacker with control of the network. In the event that an individual chunk fails integrity verification, it is re-requested from the OS Recovery Server 11 times, before giving up and displaying an error.”
Are you able to leave the recovery environment to use the Console App to find any relevant system log details?
View log messages in Console on Mac - Apple Support
“Use Console to view log messages collected by your computer and other connected devices. These log messages may deal with system events, dialog text, errors, status, and other communications. If a problem occurs, you may be able to find information about the cause of the problem by viewing either log messages or activities.”
I hope this helps.