Like something on the tip of your tongue that you just can't stop thinking about, I continued to search for an answer to this. Though I never found the page that had made everything so simple, I found a couple of pages that gave me enough hints to cobble together what I had in mind. I'd add at least one of the links here, but since it isn't directly related to Russian or the Cyrillic alphabet, I'll just provide an explanation here. If you are using Windows 7, you should be able to access "Symbols" from your Insert tab. I'll add some screenshots so you can know what I mean. Key sections have been highlighted in green.
First, you'll want to go to your Insert tab and click on the dropdown box for "Symbols":
From there, you'll want to click on "More Symbols..."
This will open up a window for you that looks like this:
Notice how the "Combining Diacritical Marks" in the dropdown "Subset" menu has been highlighted. You may find other accent marks that look like an acute accent mark, but this is the one you want. (It is number 0301, if you just want to type it into the field for character code to bring it up.) You should already find that it has been given a predesignated shortcut key, but if you prefer another, select the button for Shortcut key and create your own. ALT+Ctrl+э is what I chose for my shortcut. You can choose any you like as long as it isn't already assigned to another character.
Now you are ready to begin typing. Make sure you are using the keyboard you want. This will likely look different on different computers, but if you're using Windows 7 and MS Office 7, it might look something like the following at the bottom left and right of your screen (depending, of course, on how you have things configured):
If you feel certain you're about to use the correct keyboard, you can begin typing ...
Once you've typed the letter that you'd like to put an accent on, press your shortcut key combination ...
and an accent should appear over the last letter you typed. You can continue typing without making any additional keyboard strokes ...
You'll have to do this a bit differently in PowerPoint (at least the MS Office 2007 version). You won't be able to use a shortcut key, but you can access the same group of symbols, including the aforementioned #0301 character. What you will need to do is position your cursor immediately after the letter you want to accent and then insert it the long way -- pull up the Symbols box, find the character you need, and insert it. The character immediately preceding the cursor will become accented. If you want to preserve formatting inside of the textboxes you've created in PowerPoint, this is likely the best way to do it. I do not recommend copying and pasting a previously accented letter from Word, but go ahead and try it if you really want to. I think you'll see what I mean.
So, there you have it. Hope this helped someone out there.