Gregory, let me ask a question:
How important is this to you? Here is why I ask...
I often offer to perform testing for someone, go through several hours of tests, post a response, and never ever hear back from that person.
Bottom line is that I have the knowledge to make this work - if it is possible. The "if it is possible" is the only question mark for me. I'm willing to test this, but only if I know that it will really help you

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Some more info...
On a UEFI based system, you would normally have 4 partitions. On legacy BIOS, as is your situation, you would have 2 partitions: the Windows partition and a System Reserved partition. I can easily create an installation that forces Windows to create only a single partition, omitting the reserved partition, to see if it will work.
But I want to know that this going to really help you before I make all that effort.
Before we go any further, can I inquire why you even want to do this? The reserved partition is only ~500MB in size so if space savings is the concern, it seems hardly worth the effort to me. If you have some other concern, let me know what that is and possibly I can make some other recommendation that satisfies your needs.
EDIT: One additional note - for UEFI based systems, forget about it. It's not going to happen

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