ITunes Match reboots my computer

Question

First, the technical specs:
Model Name: iMac
Model Identifier: iMac13,2
Processor Name: Intel Core i7
Processor Speed: 3.4 GHz
Number of Processors: 1
Total Number of Cores: 4
Memory: 32 GB
Boot ROM Version: IM131.010A.B05
OS: Yosemite 10.10.3
iTunes: 12.1.2.27
My iTunes library is located on an external LaCie 3TB Thunderbolt drive.
For some time I've been trying to determine why I could not get iTunes Match to work properly when syncing with my iOS devices (an iPhone 5 and iPad 2 (maybe). Both are on iOS 8.3. After much poking and prodding, I realized that the issue was due to my having over 35,000 songs in iTunes. I spent a lot of time paring down my library until I got down to about 24,000 songs (this includes the 200 or so purchases on my Apple ID, so I should now have plenty of buffer).
I also wiped out the iTunes Match data from prior syncs by clearing out my library then deleting the songs that iTunes indicated were up on Match. I wanted a fresh sync of data.
However, every time I try to launch iTunes Match, whenever I get about a third of the way through Step 1, my Mac reboots. It appears as if Yosemite freezes, but instead of the grey screen of death, the computer just reboots. I've tried looking for crash logs, but there is nothing I can find. Even though I am not an expert by any means, I can usually find the crash log or even the entry in some log somewhere I can grab a screen cap of to send to the more tech savvy. But right now it looks like nothing's getting recorded and Yosemite is treating the reboot as just that: a reboot.
In my attempts to troubleshoot, I have reinstalled Yosemite, reinstalled iTunes, deleted and rebuilt my iTunes library database. I've run Disk First Aid on both my boot drive (through recovery mode) and my Thunderbolt drive. I've even re-imported every song, twice, and culled any file that caused an issue on import. I've scoured my collection for not only absolute duplicates, but also, when the choice came between a song contained in a full album and a song in a partial album, I deleted the partial album's file.
At this point, I've run out of ideas on troubleshooting. Well, maybe not quite. The only variable I did not check out was the presence of my husband's purchased music. Ideally it should be ok, since we linked our accounts (through the family feature). Yet this was a newer feature and this is the first time I've tried to re-sync iTunes Match from scratch since the Family feature went live.
In any event, any suggestions or advice would be most welcome. I rather enjoyed iTunes Match, and am loathe to give it up. Yet I can't see paying for a service that won't work. If you need to look at logs, I'll be happy to provide. Key words to look for would help greatly.
Thank you.
Edit: I also repaired permissions as part of my troubleshooting.
Edit: I removed all purchased music. I also deauthorized and reauthorized my iMac and logged out of and back into my account (I only have one account). iTunes Match still stalls about ⅓ of the way in to Stage 1. I stopped iTunes Match from processing right now.

Answer 1

These instructions must be carried out as an administrator. If you have only one user account, you are the administrator.
Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad and start typing the name.
Step 1
For this step, the title of the Console window should be All Messages. If it isn't, select
          SYSTEM LOG QUERIES ▹ All Messages
from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar at the top of the screen.
In the top right corner of the Console window, there's a search box labeled Filter. Initially the words "String Matching" are shown in that box. Enter "BOOT_TIME" (without the quotes.)
Each message in the log begins with the date and time when it was entered. Select the BOOT_TIME log message that corresponds to the last boot time when you had the problem. Now clear the search box to reveal all messages. Select the ones logged before the boot, during the time something abnormal was happening. Copy them to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressing command-V.
For example, if the system was unresponsive or was failing to shut down for three minutes before you forced a restart, post the messages timestamped within three minutes before the boot time, not after. Please include the BOOT_TIME message at the end of the log extract—not at the beginning.
If there are long runs of repeated messages, please post only one example of each. Don’t post many repetitions of the same message.
When posting a log extract, be selective. A few dozen lines are almost always more than enough.
Some private information, such as your name, may appear in the log. Anonymize before posting.
Please don't indiscriminately dump thousands of lines from the log into this discussion.
Please don't post screenshots of log messages—post the text.
Step 2
In the Console window, select
          DIAGNOSTIC AND USAGE INFORMATION ▹ System Diagnostic Reports
(not Diagnostic and Usage Messages) from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar.
There is a disclosure triangle to the left of the list item. If the triangle is pointing to the right, click it so that it points down. You'll see a list of reports. A crash report has a name that begins with the name of the crashed process and ends in ".crash". A panic report has a name that begins with "Kernel" and ends in ".panic". A shutdown stall report has a name that ends in ".shutdownstall". Select the most recent of each, if any. The contents of the report will appear on the right. Use copy and paste to post the entire contents—the text, not a screenshot. It's possible that none of these reports exists.
I know the report is long, maybe several hundred lines. Please post all of it anyway.
If you don't see any reports listed, but you know there was a crash or panic, you may have chosen Diagnostic and Usage Messages from the log list. Choose DIAGNOSTIC AND USAGE INFORMATION instead.
In the interest of privacy, I suggest that, before posting, you edit out the “Anonymous UUID,” a long string of letters, numbers, and dashes in the header of the report, if it’s present (it may not be.)
Please don’t post other kinds of diagnostic report—they're very long and rarely helpful.
When you post the log extract or the crash report, you might see an error message on the web page: "You have included content in your post that is not permitted," or "The message contains invalid characters." That's a bug in the forum software. Please post the text on Pastebin, then post a link here to the page you created.