Apparently, I'm running out of space on my main partition of the two, so I want to shrink the second one to make room.
The problem is, how do I "move files over" on the second partition further into the harddrive to make room for the OS? And no, I'm not willing to do a clean install just to make the main partition bigger.
This is not quite so easy, and for two reasons. The first is that you can't do what you desire. That is, you cannot move files to the end of the second Partition and then move the start of that Partition further out on the drive. All the common tools to shrink a Partition will shrink the END of it, not the start.
The second problem is that Windows, which has some tools to shrink and expand a Partition, will NOT do those things on your BOOT Partition (the C: drive). It's Windows' way of being cautious about manipulating a critical set of disk files. So, even if you could manage to create some Unallocated Space right after the end of the first Partition (C: drive), Windows does not have a way to Expand that Partition to include that space.
What to do? Well, what you want CAN be done by third-party software you must buy. Partition Magic comes to mind, and I'm sure there are others. These tools CAN re-size and move Partitions around, including expanding the Boot Partition (C: drive) to use the space it empties out for you. The downside is, they cost a bit of money - not free.
BIG NOTE: When doing this kind of work sometimes things go wrong. Hence it is ALWAYS recommended that you make a good backup copy of ALL the data on ALL your Partitions (including the OS, etc.) and ensure that they are valid backups you can use. Then if bad things happen you can restore from there.